Question

If (x - 2) is a divisor of p(x) = [tex] {3x}^{2} - kx + 10, Find the value of K. ​

Answer 1

Answer:

$\huge{\pink{\green {\sf\boxed{Therefore\: K = 11}}}}$

Step-by-step explanation:

$\huge{\pink {\sf\underline{SOLUTION→}}}$

$\bold{Given:} </p><p>Divisor = (x - 2), </p><p>{Polinomial(x) = {3x}^{2} - Kx + 10}$

$\bold{To \:Find:} \:{Value\: of\: K =? }$

$\Large\boxed{According\:to\: given\: question⟹}$

${(x - 2) is \:divisor \:of \:P (x)= {3x}^{2} - Kx + 10}$

K =?

So, $</strong><strong>⟹</strong><strong> {</strong><strong>P</strong><strong>(</strong><strong>x</strong><strong>)</strong><strong> </strong><strong>=</strong><strong> </strong><strong>0</strong><strong>}</strong><strong> </strong><strong>$

$⟹ {</strong><strong>x</strong><strong> </strong><strong>-</strong><strong> </strong><strong>2</strong><strong>= 0}$

$⟹ </strong><strong>{</strong><strong>x</strong><strong> </strong><strong>= </strong><strong>2</strong><strong>}$

Putting ${</strong><strong>x</strong><strong> </strong><strong>=</strong><strong> </strong><strong>2</strong><strong>}$ in the above polynomial.

$⟹ {P(x) =</strong><strong>{</strong><strong>3x</strong><strong>}</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong> </strong><strong>-</strong><strong> </strong><strong>Kx</strong><strong> </strong><strong>+</strong><strong> </strong><strong>10</strong><strong>}$

$⟹ {</strong><strong>0</strong><strong> = </strong><strong>3</strong><strong>*</strong><strong>{</strong><strong>(</strong><strong>2</strong><strong>)</strong><strong>}</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong> </strong><strong>-</strong><strong> </strong><strong>K</strong><strong>*</strong><strong>(</strong><strong>2</strong><strong>)</strong><strong> </strong><strong>+</strong><strong> </strong><strong>10</strong><strong>}$

$⟹ {0= 12 - 2K + 10}$

$⟹ {0 = 22 - 2K}$

$⟹ {-22 = - 2k}$

$⟹ {K = \dfrac{22}{2}}$

$⟹ {K = 11}$

$\huge {\red{\boxed{ANSWER, K = 11}}}$

$\Large\boxed{SOLVED}$

#Be_Brainly

Answer 2

$\bf{\underline{\underline{Answer:}}}$

∴ $\bf{K=\dfrac{3}{2}}$

$\bf{\underline{\underline{Step\: by\: step\: explanation:}}}$

if x-1 (i.e. x=1) is a factor of p(x) then

p(x)=0

i.e. p(1)=0

$\bf{\underline{\underline{According\: to\: Question:}}}$

Substituting the value of x in p(x)

p(1) = k${(1)}^{2}$ - 3(1) + k

0 = k×1 - 3 + k

0 = k + k - 3

0 = 2k - 3

0+3 = 2k

3 = 2k

$⟹\bf{k=\dfrac{3}{2}}$