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

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) = x² - 1, x = 1, -1

p(1) = 1² - 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) = x², x = 0

p(0) = 0² = 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) = 3x² - 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).

☛ Check: CBSE NCERT Solutions Class 9 Maths Chapter 2

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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) = x² − 1, x = −1,2 are zeros of p(x) = (x + 1) (x − 2), x = 0 is a zero of p(x) = x², x = -m/l is a zero of p(x) = lx + m, x = −1/√3 is a zero of p(x) = 3x² - 1 and x = 2/√3 is not a zero of p(x) = 3x² - 1, x = 1/2 is not a zero of p(x) = 2x +1.

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