# Verify whether the following are zeroes of the polynomial, indicated against them.

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

(ii) p(x) = 5x - π , x = 4/5

(iii) p(x) = x^{2} - 1, x = 1, -1

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

(v) p(x) = x^{2} , x = 0

(vi) p(x) = lx + m, x = -(m/l)

(vii) p(x) = 3x^{2} - 1, x = -(1/√3), 2/√3

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

**Solution:**

In general, we say that a zero of a polynomial p(x) is a number c such that p(c) = 0.

**(i)** p(x) = 3x + 1, x = -(1/3)

p(-1/3) = 3 × (-1/3) + 1 = 0

Therefore, -1/3 is a zero of p(x).

**(ii)** p(x) = 5x - π, x = 4/5

p(4/5) = 5(4/5) - π

We know that, π = 22/7

Thus, p(4/5) = 4 - 22/7 ≠ 0

Therefore, 4/5 is not a zero of p(x).

**(iii)** p(x) = x^{2} - 1, x = 1, -1

p(1) = 1^{2} - 1 = 0

p(-1) = (-1)^{2} - 1 = 1 - 1 = 0

Therefore, 1 and -1 are zeroes of p(x).

**(iv)** 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

Therefore, -1 and 2 are zeroes of p(x).

**(v)** p(x) = x^{2}, x = 0

p(0) = 0^{2} = 0

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

**(vi)** p(x) = lx + m, x = -(m/l)

p(-m/l) = l × (-m/l) + m

⇒ -m + m = 0

Therefore, -(m/l) is a zero of p(x).

**(vii)** p(x) = 3x^{2} - 1, x = -(1/√3), 2/√3

p(-1/√3) = 3 × (-1/√3)^{2} - 1

= 3 × (1/3) - 1 = 1 - 1 = 0

Therefore, -1/√3 is a zero of p(x).

p(2/√3) = 3 × (2/√3)^{2} - 1

= 3 (4/3) - 1

= 4 - 1 = 3 ≠ 0

Therefore, 2/√3 is not a zero p(x).

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

p(1/2) = 2 × (1/2) + 1

= 1 + 1 = 2 ≠ 0

Therefore, 1/2 is not a zero of p(x).

**Video Solution:**

## Verify whether the following are zeroes of the polynomial, indicated against them. (i) p(x) = 3x + 1, x = -(1/3) (ii) p(x) = 5x - π , x = 4/5 (iii) p(x) = x² - 1, x = 1, -1 (iv) p(x) = (x + 1)(x - 2), x = -1, 2 (v) p(x) = x² , x = 0 (vi) p(x) = lx + m, x = -(m/l) (vii) p(x) = 3x² - 1, x = -(1/√3), 2/√3 (viii) p(x) = 2x + 1, x = 1/2

### NCERT Solutions Class 9 Maths - Chapter 2 Exercise 2.2 Question 3:

**Summary:**

For the given polynomials we see that, x = -1/3 is a zero of p(x) = 3x + 1, x = 4/5 is not a zero of p(x) = 5x − π, x = 1, -1 are zeros of p(x) = x^{2} − 1, x = −1,2 are zeros of p(x) = (x + 1) (x − 2), x = 0 is a zero of p(x) = x^{2}, x = -m/l is a zero of p(x) = lx + m, x = −1/√3 is a zero of p(x) = 3x^{2} - 1 and x = 2/√3 is not a zero of p(x) = 3x^{2} - 1, x = 1/2 is not a zero of p(x) = 2x +1.