RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A

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RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A

Exercise 10A

Question 1:

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

(ii) 2x²+ 52x-√3=0
⇒ 4x²+5x-2√3=0
Clearly is 4x²+5x-2√3=0 a quadratic polynomial.
∴ 2x²+ 52x-√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)13x²+15x-2=0
⇒ 5x²+3x-2=0
Clearly, 5x²+3x-2=0 is a quadratic equation.
13x²+15 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-6x=3
⇒ x²-3x-6 =0
And (x²-3x-6)Being a polynomial of degree 2, it is a quadratic polynomial.
Hence, x-6x=3 is a quadratic equation.

(vii) x+2x= x²
⇒ x³-x²-2 =0
And (x³-x²-2 =0) being a polynomial of degree 3, it is not a quadratic polynomial.
Hence, x+2x= x² is not a quadratic equation.

(viii) x2−1×2=5 ⇒ x⁴ -1=5x²
⇒x⁴-5x²-1 =0
And (x⁴-5x²-1 =0) being a polynomial of degree 4.
Hence x2−1×2=5 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

(ii) On substituting x=13 in the equation, we get

(iii) On substituting x=−12 in the equation , we get

Question 3:
Since x = 1 is a solution of x²+kx+3=0 it must satisfy the equation.

Hence the required value of k = -4
Question 4:
Since x=34 is a root of  ax²+bx-6=0, we have


Again x = -2 being a root of ax²+bx-6=0, we have

Multiplying (2) by 4 adding the result from (1), we get
11a = 44 ⇒ a = 4
Putting a = 4 in (1), we get

Question 5:

Question 6:

Question 7:

Hence, 9 and -9 are the roots of the equation 3x²-243=0.
Question 8:

Hence, -5 and -7 are the roots of x²+12x+35=0.
Question 9:

Hence, 11 and 7 are the roots of equation x²=18x-77
Question 10:

Hence, x=−13 is the repeated root of the equation 9x²+6x+1=0
Question 11:

Hence,  is the repeated root of the equation
Question 12:

Hence, x=−32, x=−12are the roots of 6x²+11x+3=0
Question 13:

Hence, x=43 and x=−32 are the roots of equation 6x²+x-12=0

Question 14:

Hence, x=−13 and 1 are the roots of the equation 3x²-2x-1=0.
Question 15:

Hence, x=23 and x=−12are the roots of equation 6x²-x-2=0.
Question 16:

Hence, x=−116 and x=23 are the roots of 48x²-13x-1=0.
Question 17:

Hence, x=−53 and x=-2 are the roots of the equation 3x²+11x+10=0
Question 18:

Hence,x=254 and x=-4 are the roots of the equation 4x²-9x=100.
Question 19:

Hence,  x=49 and 2 are the roots of the equation 9x²-22+8=0
Question 20:

Hence,  x=75 and x=−43 are the roots of the given equation 15x²-28=x.
Question 21:

Hence, x=13 and -4 are the roots of the given equation.
Question 22:

Hence, 1 and  √2 are the roots of the given equation
Question 23:

Question 24:

Question 25:

Hence, −7√3 and 7√7 are the roots of given equation.
Question 26:

Hence, -√7 and 137√7 are the roots of given equation.
Question 27:

Hence, 26√3 and  −6√8are the roots of given equation.
Question 28:

Hence, 5 and −75are the roots of given equation
Question 29:

Hence, −15 and 12are the roots of given equation.
Question 30:

Hence, 2 and  12 are the roots of given equation.
Question 31:

Hence, −ba and cb are the roots of given equation.
Question 32:

Hence, −1a2 and 1b2are the roots of given equation.
Question 33:

Hence, 3a4b and −2b3a are the roots of given equation.
Question 34:

Hence, a22 and b22are the roots of given equation.
Question 35:

Hence, 2 and 1 are the roots of the given equation
Question 36:

Hence, -9 and 7 are the roots of the given equation
Question 37:

Hence, -4 and 94 are the roots of the given equation
Question 38:

Hence  4013 and 6 are the roots of the given equation
Question 39:

Hence, 4 and −29 are the roots of the given equation
Question 40:

Hence, 3 and 43 are the roots of the given equation.
Question 41:

Hence, 5 and 12 are the roots of the given equation.
Question 42:
Putting  the given equation become

Case I:

Case II:

Hence, −32 and -2 are the roots of the given equation
Question 43:

Putting  the given equation become

Case I:

Case II:

Hence, -1 and −235 are the roots of the given equation
Question 44:
On putting  the given equation become

Case I:

Case II:

Hence, -10 and −15 are the roots of the given equation.
Question 45:
Putting  the given equation become

Case I:

Case II:

Hence, -1 and 18 are the roots of the given equation
Question 46:
The given equation

Hence, (a+b) and (a+b)2 is the roots of the given equation
Question 47:

Hence, a+bab and 2a+b are the roots of the given equation
Question 48:

Hence, -2,0 are the roots of the given equation
Question 49:

Hence,  12 and 12 are the roots of the given equation
Question 50:

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