Question

If (x – 2k) is a factor of f(x), which of the following must be true? f(2k) = 0 f(–2k) = 0 A root of f(x) is x = –2k. A y intercept of f(x) is x = 2k.

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{(x-2k) is a factor of f(x)}$

$\underline{\textbf{To find:}}$

$\textsf{Which of the following is true}$

$\mathsf{(i)\;f(2k)=0}$

$\mathsf{(ii)\;f(-2k)=0}$

$\mathsf{(iii)\;A\;root\;of\;f(x)\;is\;x=-2k}$

$\mathsf{(iv)\;y\;intercept\;of\;f(x)\;is\;x=2k}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Factor used:}}$

$\boxed{\textbf{(x-a) is a factor of P(x) iff P(a)=0}}$

$\textsf{As per given data,}$

$\textsf{(x-2k) is a factor of f(x)}$

$\textsf{By factor theorem,}$

$\mathsf{f(2k)=0}$

$\underline{\textbf{Answer:}}$

$\mathsf{f(2k)=0}$

$\underline{\textbf{Find more:}}$

Verify whether (x + 1), (x – 2) and (x + 3) are the factors of the polynomial x3 + 2x2– 5x – 6 without actual

division. with the explanation

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