Question

$find \: the \: value \: of \: k \: \: if \: 2 - 1 \: is \: a \: factor \: of \: p(x) = {kx}^{2} - 3x + k$
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Answer 1

★Correct Question :

$find \: the \: value \: of \: k \: if \: x - 1 \: is \: a \: factor \: of \: p(x) = {kx}^{2} - 3x + k$

★ Given :

x-1 is a factor of p(x)

★ To find :

value of k

★ Solution :

we know that, if (x-1) is a factor of p(x) , then p(1) should be equal to 0 as per factor theorem.

p(x) = kx² - 3x + k

p(1) = k (1)² - 3 + k

= 2k - 3

2k - 3 = 0

2k = 3

$\bold{k = \frac{3}{2} = 1.5$

★ Verification :

p(x) = 1.5x² -3x + 1.5

p(1) = 1.5 -3 +1.5

= 3-3

= 0

Hence verified .

Answer 2

K=3/2

Hope it will help you.