# Polynomials – Exercise 2.2 – (MATHEMATICS) – 9th Class

**Execise. 2.2**

**1. Find the value of the polynomial 5x – 4x² +3 at**

(i) x = 0

(ii) x = -1

(iii) x = 2

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**Sol.**Let f (x) = 5x – 4x² + 3.

(i) f (0) = 0 – 0 + 3 = 3

(ii) f (-1) = – 5 – 4 + 3 = – 6

(iii) f (2) = 10 – 16 + 3 = – 3

**2. Find p(0), p(1) for each of the following polynomials:**

(i) p(y) = y² – y + 1

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Ans. – p(0) = 0 – 0 + 1 = 1 ; p (1) = 1 – 1 + 1 = 1;

p (2) = 4 – 2 + 1 = 3.

(ii) p(t) = 2 + t + 2t² – t³

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Ans. – p(0) = 2 + 0 + 0 – 0 = 2; p(1) = 2 + 1 + 2 – 1 = 4;

p (2) = 2 + 2 + 8 – 8 = 4

(iii) p (x) = x³

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Ans. – p (0) = 0; p(1) = 1; p(2) = 8

(iv) p(x) = (x-1)(x+1)

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Ans. – p(0) = (0 – 1) (0 + 1 ) = – 1 ; p (1) = (1-1)(1+1) = 0 ;

p(2) = ( 2-1) (2 + 1) = 3

**3. Verify whether the following are zeroes of the polynomial, indicated again indicated against them.**

(i) p(x) = 3x + 1, x =

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Ans.-

Hence, is a zero of the polynomial p(x).

(ii) p(x) = 5x – π , x =

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Ans.-

Hence, is not a zero of the polynomial p (x)

(iii) p(x) =x

^{2}– 1 , x = 1 , -1

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Ans.- p(1) = 1-1 = 0 and p(-1) = 1 -1 = 0

Hence , x = 1 and x = -1 are zeroes of the polynomial p(x)

(iv) p(x) = (x +1 ) (x-2) , x = -1 , 2

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Ans.- p(-1) = (-1 + 1 ) (-1-2) = 0 and p(2) = (2+1) (2-2) = 0

Hence, x = -1 and x=2 are zeroes of the polynomial p(x).

(v) p(x) = x², x= 0

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Ans.- p(0) = 0 . Hence, x = 0 is a zero of the polynomial p (x).

(vi) p(x) = lx + m, x =

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Ans.-

Hence, x = – is a zero of the polynomial p(x) .

(vii) p(x) = 3x² – 1, x = –

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Ans.-

and

Hence, is a zero and is not a zero of the polynomial p(x)

(viii) p(x) = 2x + 1, x=

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Ans.-

Hence, is not a zero of the polynomial p(x).

**4. Find the zero of the polynomial in each of the following cases:**

(i) p(x) = x + 5

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Ans. – For zero, p(x) = 0 ⇒ x + 5 = 0

⇒ x = -5 is a zero of the polynomial p(x).

(ii) p(x) = x – 5

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Ans. – For zero , p(x) = 0 ⇒ x – 5 = 0

⇒ x = 5 is a zero of the polynomial p(x).

(iii) p(x) = 2x + 5

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Ans. – For zero, p(x) = 0 ⇒ 2x = 5 = 0

⇒ is a zero of the polynomial p(x).

(iv) p(x) = 3x – 2

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Ans. – For zero, p(x) = 0 ⇒ 3x – 2 = 0

is a zero of the polynomial p(x).

(v) p(x) = 3x

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Ans. – For zero , p(x) = 0 ⇒ 3x = 0

⇒ x = 0 is a zero of the polynomial p(x).

(vi) p(x) = ax, a ≠ 0

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Ans. – For zero , p(x) = 0 ⇒ ax = 0

⇒ x = 0 , as a ≠ 0

Therefore, x = 0 is a zero of the polynomial p (x).

(vii) p(x) = cx + d, c≠0, c, d are real numbers.

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Ans. – For zero, p(x) = 0 ⇒ cx + d = 0

Therefore, is a zero of the polynomial p(x).