RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations

Here you can get solutions of RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations. These Solutions are part of RS Aggarwal Solutions Class 10. we have given RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations download pdf.

RS Aggarwal Solutions Class 10 Chapter 10

Question 1:

(i)   x2-x+3=0 is a quadratic polynomial.
∴  x2-x+3=0 is a quadratic equation.

(ii) 2x2+ [latex]\frac { 5 }{ 2 }   [/latex]x-√3=0
⇒ 4x2+5x-2√3=0
Clearly is 4x2+5x-2√3=0 a quadratic polynomial.
∴ 2x2+ [latex]\frac { 5 }{ 2 }   [/latex]x-√3=0 is a quadratic equation.

(iii) √2x2+7x+5√2=0 is a quadratic polynomial.
∴ √2x2+7x+5√2=0 is a quadratic equation.

(iv)[latex]\frac { 1 }{ 3 }   [/latex]x2+[latex]\frac { 1 }{ 5 }   [/latex]x-2=0
⇒ 5x2+3x-2=0
Clearly, 5x2+3x-2=0 is a quadratic equation.
[latex]\frac { 1 }{ 3 }   [/latex]x2+[latex]\frac { 1 }{ 5 }   [/latex] is a quadratic equation.

(v) x2-3x-√x+4=0 is not a quadratic polynomial since it contains √x, in which power 1/2 of x is not an integer.
∴ x2-3x-√x+4=0 is not a quadratic equation.

(vi) x-[latex]\frac { 6}{ x }   [/latex]=3
⇒ x2-3x-6 =0
And (x2-3x-6)Being a polynomial of degree 2, it is a quadratic polynomial.
Hence, x-[latex]\frac { 6}{ x }   [/latex]=3 is a quadratic equation.

(vii) x+[latex]\frac { 2}{ x }   [/latex]= x2
⇒ x3-x2-2 =0
And (x3-x2-2 =0) being a polynomial of degree 3, it is not a quadratic polynomial.
Hence, x+[latex]\frac { 2}{ x }   [/latex]= x2 is not a quadratic equation.

(viii) [latex]{ x }^{ 2 }-\frac { 1 }{ { x }^{ 2 } } =5  [/latex] ⇒ x4 -1=5x2
⇒x4-5x2-1 =0
And (x4-5x2-1 =0) being a polynomial of degree 4.
Hence [latex]{ x }^{ 2 }-\frac { 1 }{ { x }^{ 2 } } =5  [/latex] is not a quadratic equation.

Question 2:
The given equation is 3x2+2x-1=0
(i) On substituting x = -1 in the equation, we get
rs-aggarwal-class-10-solutions-quadratic-equations-10a-q2-1
(ii) On substituting [latex]x=\frac { 1 }{ 3 }   [/latex] in the equation, we get
rs-aggarwal-class-10-solutions-quadratic-equations-10a-q2-2
(iii) On substituting [latex]x=-\frac { 1 }{ 2 }    [/latex] in the equation , we get
rs-aggarwal-class-10-solutions-quadratic-equations-10a-q2-3

Question 3:
Since x = 1 is a solution of x2+kx+3=0 it must satisfy the equation.
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence the required value of k = -4
Question 4:
Since [latex]x=\frac { 3 }{ 4 }   [/latex] is a root of  ax2+bx-6=0, we have
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Again x = -2 being a root of ax2+bx-6=0, we have
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Multiplying (2) by 4 adding the result from (1), we get
11a = 44 ⇒ a = 4
Putting a = 4 in (1), we get
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Question 5:
RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Question 6:
RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Question 7:
RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, 9 and -9 are the roots of the equation 3x2-243=0.
Question 8:
RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, -5 and -7 are the roots of x2+12x+35=0.
Question 9:
RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, 11 and 7 are the roots of equation x2=18x-77
Question 10:
Solution of RS Aggarwal Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]x=-\frac { 1 }{ 3 }    [/latex] is the repeated root of the equation 9x2+6x+1=0
Question 11:
Solution of RS Aggarwal Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence,  is the repeated root of the equation
Question 12:
Solution of RS Aggarwal Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]x=-\frac { 3 }{ 2 }   [/latex], [latex]x=-\frac { 1 }{ 2 }   [/latex]are the roots of 6x2+11x+3=0
Question 13:
Solution of RS Aggarwal Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]x=\frac { 4 }{ 3 }   [/latex] and [latex]x=-\frac { 3 }{ 2 }   [/latex] are the roots of equation 6x2+x-12=0

Question 14:
RS Aggarwal Solutions Class 10 2017 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]x=-\frac { 1 }{ 3 }   [/latex] and 1 are the roots of the equation 3x2-2x-1=0.
Question 15:
RS Aggarwal Solutions Class 10 2017 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]x=\frac { 2 }{ 3 }   [/latex] and [latex]x=-\frac { 1 }{ 2 }   [/latex]are the roots of equation 6x2-x-2=0.
Question 16:
RS Aggarwal Solutions Class 10 2017 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]x=-\frac { 1 }{ 16 }   [/latex] and [latex]x=\frac { 2 }{ 3 }   [/latex] are the roots of 48x2-13x-1=0.
Question 17:
RS Aggarwal Solutions Class 10 2017 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]x=-\frac { 5 }{ 3 }   [/latex] and x=-2 are the roots of the equation 3x2+11x+10=0
Question 18:
Class 10 RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence,[latex]x=\frac { 25 }{ 4 }   [/latex] and x=-4 are the roots of the equation 4x2-9x=100.
Question 19:
Class 10 RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence,  [latex]x=\frac { 4 }{ 9 }   [/latex] and 2 are the roots of the equation 9x2-22+8=0
Question 20:
Class 10 RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence,  [latex]x=\frac { 7 }{ 5 }   [/latex] and [latex]x=-\frac { 4 }{ 3 }   [/latex] are the roots of the given equation 15x2-28=x.
Question 21:
RS Aggarwal Class 10 Maths Book Solutions pdf Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]x=\frac { 1 }{ 3 }   [/latex] and -4 are the roots of given equation .
Question 22:
RS Aggarwal Class 10 Maths Book Solutions pdf Chapter 10 Quadratic Equations Ex 10a
Hence, 1 and  √2 are the roots of the given equation
Question 23:
RS Aggarwal Class 10 Maths Book Solutions pdf Chapter 10 Quadratic Equations Ex 10a
Question 24:
RS Aggarwal Class 10 Book pdf download Chapter 10 Quadratic Equations Ex 10a
Question 25:
RS Aggarwal Class 10 Book pdf download Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]\frac { -\sqrt { 7 }  }{ 3 }      [/latex] and [latex]\frac { \sqrt { 7 }  }{ 7 }     [/latex] are the roots of given equation.
Question 26:
RS Aggarwal Class 10 Book pdf download Chapter 10 Quadratic Equations Ex 10a
Hence, -√7 and [latex]\frac { 13\sqrt { 7 }  }{ 7 }     [/latex] are the roots of given equation.
Question 27:
RS Aggarwal Class 10 Book pdf download Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]\frac { 2\sqrt { 6 }  }{ 3 }     [/latex] and  [latex]\frac { -\sqrt { 6 }  }{ 8 }     [/latex]are the roots of given equation.
Question 28:
Class 10 Maths RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, 5 and [latex]-\frac { 7 }{ 5 }    [/latex]are the roots of given equation
Question 29:
Class 10 Maths RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]-\frac { 1 }{ 5 }    [/latex] and [latex]\frac { 1 }{ 2 }    [/latex]are the roots of given equation.
Question 30:
Class 10 Maths RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, 2 and  [latex]\frac { 1 }{ 2 }    [/latex] are the roots of given equation.
Question 31:
Class 10 Maths RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]-\frac { b }{ a }    [/latex] and [latex]\frac { c }{ b }    [/latex] are the roots of given equation.
Question 32:
Class 10 Maths RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]\frac { -1 }{ { a }^{ 2 } }     [/latex] and [latex]\frac { 1 }{ { b }^{ 2 } }     [/latex]are the roots of given equation.
Question 33:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]\frac { 3a }{ 4b }    [/latex] and [latex]\frac { -2b }{ 3a }    [/latex] are the roots of given equation.
Question 34:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]\frac { { a }^{ 2 } }{ 2 }      [/latex] and [latex]\frac { { b }^{ 2 } }{ 2 }      [/latex]are the roots of given equation.
Question 35:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence, 2 and 1 are the roots of the given equation
Question 36:
Class 10 RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, -9 and 7 are the roots of the given equation
Question 37:
Class 10 RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, -4 and [latex]\frac { 9 }{ 4 }    [/latex] are the roots of the given equation
Question 38:
Class 10 RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence  [latex]\frac { 40 }{ 13 }    [/latex] and 6 are the roots of the given equation
Question 39:
Class 10 RS Aggarwal Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, 4 and [latex]-\frac { 2 }{ 9 }    [/latex] are the roots of the given equation
Question 40:
RS Aggarwal Solutions Class 10 2017 Chapter 10 Quadratic Equations Ex 10a
Hence, 3 and [latex]\frac { 4 }{ 3 }    [/latex] are the roots of the given equation.
Question 41:
RS Aggarwal Solutions Class 10 2017 Chapter 10 Quadratic Equations Ex 10a
Hence, 5 and [latex]\frac { 1 }{ 2 }    [/latex] are the roots of the given equation.
Question 42:
Putting RS Aggarwal Solutions Class 10 2017 Chapter 10 Quadratic Equations Ex 10a the given equation become
RS Aggarwal Solutions Class 10 2017 Chapter 10 Quadratic Equations Ex 10a
Case I:
Solution of RS Aggarwal Class 10 Chapter 10 Quadratic Equations Ex 10a
Case II:
Solution of RS Aggarwal Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]-\frac { 3 }{ 2 }    [/latex] and -2 are the roots of the given equation
Question 43:
Solution of RS Aggarwal Class 10 Chapter 10 Quadratic Equations Ex 10a
Putting Solution of RS Aggarwal Class 10 Chapter 10 Quadratic Equations Ex 10a the given equation become
RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Case I:
RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Case II:
RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, -1 and [latex]-\frac { 23 }{ 5 }    [/latex] are the roots of the given equation
Question 44:
On putting RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a the given equation become
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Case I:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Case II:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a
Hence, -10 and [latex]-\frac { 1 }{ 5 }    [/latex] are the roots of the given equation.
Question 45:
Putting RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations Ex 10a the given equation become
RS Aggarwal Solutions Class 10 2018 Chapter 10 Quadratic Equations Ex 10a
Case I:
RS Aggarwal Solutions Class 10 2018 Chapter 10 Quadratic Equations Ex 10a
Case II:
RS Aggarwal Solutions Class 10 2018 Chapter 10 Quadratic Equations Ex 10a
Hence, -1 and [latex]\frac { 1 }{ 8 }    [/latex] are the roots of the given equation
Question 46:
The given equation
RS Aggarwal Solutions Class 10 2018 Chapter 10 Quadratic Equations Ex 10a
Hence, (a+b) and [latex]\frac { (a+b) }{ 2 }  [/latex] is the roots of the given equation
Question 47:
Maths RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, [latex]\frac { a+b }{ ab }   [/latex] and [latex]\frac { 2 }{ a+b }   [/latex] are the roots of the given equation
Question 48:
Maths RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, -2,0 are the roots of the given equation
Question 49:
Maths RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Hence,  [latex]\frac { 1 }{ 2 }    [/latex] and [latex]\frac { 1 }{ 2 }    [/latex] are the roots of the given equation
Question 50:
Maths RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations Ex 10a
Hence, 3 and 2 are the roots of the given equation.

Complete RS Aggarwal Solutions Class 10

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