NCERT Solutions For Class 9 Math Chapter – 2 Exercise – 2.2
Q1. Find the value of the polynomial (x) 5x – 4x2 + 3
- X = 0
- X = -1
- X = 2
Solution:-
- F(x) = 5x – 4x2+ 3
When x = 0
F(0) = 5(0) – 4(0) + 3
= 3
- F(x) = 5x – 4x2+ 3
F(x) = 5x – 4x2 + 3
F(-1) = 5(-1) – 4(-1)2 + 3
= -5 – 4 + 3
= -6
- F(x) = 5x – 4x2+ 3
F(2) = 5(2) – 4(2)2 + 3
F = -3
Q2. Find p(0) , p(1) and p(2) for each of the following polynomials:
- P(y) = y2– y + 1
Solution:-
P(y) = y2 – y + 1
P(0) = (0)2 – (0) + 1 = 1
P(1) = (1)2 – (1) + 1= 1
P(2) = (2)2 – (2) + 1 = 3
- P(t) = 2 + t + 2t2 – t3
Solution:-
P(0) = 2 + 0 + 2(0)2 – (0)3 = 2
P(1) = 2 + 2 + 2(1)2 – (1)3 = 2 + 1 + 2 – 1 = 4
P(2) = 2 + 2 + 2(2)2 – (2)3 = 2 + 2 + 8 – 8 = 4
- P(x) = x3
Solution:-
P(0) = (0)3 = 0
P(1) = (1)3 = 1
P(2) = (2)3 = 8
- P(x) (x-1)(x+1)
Solution:-
P(0) = (0-1)(0+1) = (-1)(1) = -1
P(1) = (1-1)(1+1) = 0(2) = 0
P(2) = (2-1)(2+1) = 1(3) = 3
Q3. Verify whether the following are zeroes of the polynomial , indicated against them.
- P(x) 3x + 1 , x = -1/3
Solution:-
P(-1/3) = 3(-1/3) + 1 = -1 + 1 = 0
-1/3 is a zero of p(x).
- P(x) = 5x – ∏, x = 4/5
Solution:-
P(4/5) = 5(4/5) = 4
4/5 is not a zero of p/(x).
- P(x) = x2– 1 , x = 1 , -1
Solution:-
P(1) = 12 – 1 = 1 – 1 = 0
P(-1) = (-1)2 – 1 = 1 – 1 = 0
1 , -1 are zeroes of p(x)
- p(x) = (x+1)(x-2) x = -1 , 2
P(-1) = (-1+1)(-1-2) = (0)(-3) = 0
P(-2) = (2+1)(2-2) = (3)(0) = 0
-1,2 are zeroes of p(x).
- P(x) = x2. x = 0
Solution:-
P(0) = 02 = 0
0 is a zero of p(x).
- P(x) /x+m , x = -m/l
Solution:-
P(-m/l) = l(-m/l) + m = -m + m = 0
-m/l is a zero of p(x).
- P(x) = 3x2– 1 , x = -1/√3 , 2/√3
Solution:-
P(-1/√3) = 3(-1/√3)2 – 1 = 3(1/3) -1 = 1 – 1 = 0
P(2/√3) = 3(2/√3)2 – 1 = 3(4/3) – 1 = 4 – 1 = 3
-1/√3 is a zero of p(x) but 2/√3 is not a zero of p(x).
- P(x) 2x + 1 , x = 1/2
Solution:-
P(1/2) = 2(1/2) + 1 = 1 + 1 = 2
1/2 is not a zero of p(x).
Q4. Find the zero of the polynomial in each of the following cases:
- P(x) x + 5
Solution:-
P(x) = x+ 5 = 0
X + 5 = 0
X = -5
-5 is a zero polynomial of the polynomial p(x).
- P(x) – x- 5
Solution:-
P(x) = x – 5
X- 5 = 0
X = 5
5 is a zero polynomial of the polynomial p(x).
- P(x) = 2x + 5
Solution:-
P(x) = 2x + 5
2x + 5 = 0
2x = -5
X = -5/2
X = -5/2 is a zero polynomial of the polynomial p(x).
- P(x) = 3x – 2
Solution:-
P(x) = 3x – 2
3x – 2 = 0
3x = 2
X = 2/3
X = 2/3 is a zero polynomial of the polynomial p(x).
- P(x) = 3x
Solution:-
P(x) = 3x
3x = 0
X= 0
0 is a zero polynomial of the polynomial p(x).
- P(x) = ax , a0
Solution:-
P(x) = ax
Ax = 0
X = 0
0 is a zero polynomial of the polynomial p(x).
- P(x) = cx + d , c ≠ 0 c , d are real numbers.
Solution:-
P(x) = cx + d
Cx + d = 0
X = -d/c
X = -d/c is a zero polynomial of the polynomial p(x).