NCERT Solutions For Class 10 Math Chapter – 2 Exercise – 2.2
Q1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients:
- x2– 2x – 8
- 4s2– 4s + 1
- 6x2– 3 – 7x
- 4u2+ 8u
- T2– 15
- 3x2– x – 4
Solution:-
- X2– 2x – 8
X2 – 4x + 2x – 8
X(x – 4) + 2(x – 4)
= (x + 2) (x – 4)
X = 4
- 4s2– 4s + 1
= 4s2 – 4s – 2s – 2s + 1
= 2s(2s – 1) -1(2s – 1)
= (2s – 1)(2s -1)
S = 1/2
- 6x2– 3 – 7x
= 6x2 – 9x + 2x – 3
= 3x(2x – 3) + 1(2x – 3)
= (3x + 1)(2x – 3)
X = 3/2
- 4u2+ 8u = 4u (u + 2)
u = -2
- T2 – 15
= t2 – (√15)2
t = -√15
- 3x2– x – 4
3x2 – 4x + 3x – 4
= x = -1
Q2. Find a quadratic polynomial each with the given numbers as the sum and product of zeroes respectively:
- 1/4 , -1
- √2 , 1/3
- 0 , √5
- 1 , 1
- -1/4 , 1/4
- 4 , 1
Solution:-
- A + b = 1/4 ab = -1
X2 – ( a – b)x + ab = x2 – 1/4x + (-1)
= 4x2 – x – 4
- A + b= √2 ab = 1/3
X2 – √2x + 1/3
= 3x2 – 3√2x + 1
- A + b = 0 ab = √5
= x2 – 0x + √5
= x2 + √5
- A + b = 1 ab = 1
= x2 – (a + b)x + ab
= x2 – x + 1
- A + b = – 1/4 ab = 1/4
= x2 – (-1/4) + 1/4
= 4x2 + x + 1
= 0
- A + b = 4 ab = 1
A + b = 4 ab = 1
X2 – 4x + 1