Question

Find k if ( x- 3) is a factor x square - kx - 2

Answer 1

Question:

Find k if (x-3) is a factor $\sf{x^{2}-kx-2}$

Answer:-

The value of k is $\sf{\frac{7}{3}}$.

Given:

• (x-3) is a factor of polynomial $\sf{x^{2}-kx-2}$

To find:

• Find the value of k

Solution:

(x-3) is a factor.

$\sf{\therefore{x=3}}$

The zero of the polynomial is 3.

$\sf{\therefore{3^{2}-k(3)-2=0}}$

$\sf{\therefore{9-3k-2=0}}$

$\sf{\therefore{-3k=-7}}$

$\sf{\therefore{k=\frac{7}{3}}}$

The value of k is $\sf{\frac{7}{3}}$.

Answer 2

$\purple{\underline{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}}$

$\rm{Find \ k \ if \ (x-3) \ is \ a \ factor \ x^{2}-kx-2}$

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$\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}$

$\rm{\blue{\boxed{\star{\red{The \ value \ of \ k \ : \ \frac{7}{3}}}}}}$

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$\sf\large\underline\pink{Given:}$

$\rm{(x-3) \ is \ a \ factor \ of \ polynomial}$

$\rm{x^{2}-kx-2}$

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$\sf\large\underline\blue{To \ Find}$

$\rm{ Value \ of \ k }$

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$\green{\underline{\underline{\red{\boxed{\boxed{\purple{\star{\sf Solution:}}}}}}}}$

$\rm{(x-3) \ is \ a \ factor.}$

$\rm{\longrightarrow{x=3}}$

$\rm{The \ zero \ of \ the \ polynomial \ is \ 3.}$

$\rm{\implies{3^{2}-k(3)-2=0}}$

$\rm{\implies{9-3k-2=0}}$

$\rm{\implies{-3k=-7}}$

$\rm{\implies{k=\frac{7}{3}}}$

$\rm{\blue{\boxed{\star{\red{The \ value \ of \ k \ : \ \frac{7}{3}}}}}}$.

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$\rm\pink{Hope \ it \ helps \ :))}$