Verify whether the following are zeroes of the polynomial, indicated a

1.	Verify whether the following are zeroes of the polynomial, indicated against them.(i) p(x) = 3x2 - 1, x = - 1/√3, 2/√3(ii) p(x) = 2x + 1, x = 1/2
Answer» (i) If x = -1/√3 and x = 2/√3 are zeroes of polynomial p(x) = 3x² − 1, then p(-1/√3) and p(2/√3) should be 0. Here, p(-1/√3) = 3(-1/√3)² - 1 = 1 - 1 = 0,and p(2/√3) = 3(2/√3)² - 1 = 3(4/3) - 1 = 4 - 1 = 3 Hence, x = -1/√3 is a zero of the given polynomial. However, x = 2/√3 is not a zero of the given polynomial. (ii) If x = 1/2 is a zero of polynomial p(x) = 2x + 1, then p(1/2) should be . Here, p(1/2) = 2(1/2) + 1 = 1 + 1 = 2 As p(1/2) ≠ 0 Therefore, x = 1/2 is not a zero of the given polynomial.

Verify whether the following are zeroes of the polynomial, indicated against them.(i) p(x) = 3x2 - 1, x = - 1/√3, 2/√3(ii) p(x) = 2x + 1, x = 1/2

Answer»

(i) If x = -1/√3 and x = 2/√3 are zeroes of polynomial p(x) = 3x² − 1, then

p(-1/√3) and p(2/√3) should be 0.

Here, p(-1/√3) = 3(-1/√3)² - 1

= 1 - 1 = 0,and

p(2/√3) = 3(2/√3)² - 1

= 3(4/3) - 1 = 4 - 1 = 3

Hence, x = -1/√3 is a zero of the given polynomial. However, x = 2/√3 is not a zero of the given polynomial.

(ii) If x = 1/2 is a zero of polynomial p(x) = 2x + 1, then p(1/2) should be .

Here, p(1/2) = 2(1/2) + 1 = 1 + 1 = 2

As p(1/2) ≠ 0

Therefore, x = 1/2 is not a zero of the given polynomial.