Question

Find the value of k if x-1 is a factor of kx2-3x+k

Answer 1

Answer:

$\large{\underline{\boxed{\sf k = \dfrac{3}{2}}}}$

Step-by-step explanation:

Given that ;

(x - 1) is a factor of the quadratic polynomial (kx² - 3x + k).

This question can be solved by plugging out the value of x, and then substituting it in the polynomial and comparing it with zero.

⇒ x - 1 = 0

⇒ x = 1

Substituting the value of x in the above polynomial.

⇒ kx² - 3x + k = 0

⇒ k(1)² - 3 * 1 + k = 0

⇒ k + k - 3 = 0

⇒ 2k = 3

⇒ k = $\sf \dfrac{3}{2}$

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Hence, the value of k is $\bf \dfrac{3}{2}$

Answer 2

Answer:

$\huge{\red{\boxed{\green{\sf{k=\frac{3}{2}}}}}}$

Step-by-step explanation:

$\huge{\red{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

${ \green{(x - 1) \: is \: a \: factor \: of \: k {x}^{2} - 3x + k = 0}} \\ \\ {\red{value \: of \: k =? }}$

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$\to if \: x - 1 \: is \: a \: factor \: of \: given \: polynomial \\ \to so \: f(x) = x - 1 = 0 \\ \to (x = 1) \\ \\ according \: to \: given \: information \\ p(x) = k {x}^{2} - 3x + k = 0 \\ p(1) = k \times {1}^{2} - 3 \times 1 + k = 0 \\ \to k - 3 + k = 0 \\ \to \: 2k - 3 = 0 \\ \to \: 2k = 3 \\ \to \: k = \frac{3}{2}$

$\huge{\red{\boxed{\green{\sf{k=\frac{3}{2}}}}}}$

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