Question

Find the value of k if (x-2) is the factor of x³+2x²-kx+10​

Answer 1

Answer:

Here, p(x) = x3 + 2x2 - kx + 10

For (x - 2) to be the factor of p(x) = x3 + 2x2 -kx + 10, p(2) = 0

Thus, (2)3 + 2(2)2 -k(2) + 10 = 0

8 + 8 - 2k + 10 = 0

k = 13

Thus p(x) becomes x3 + 2x2 - 13x + 10

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Now, (x + 5) would be the factor of p(x) iff p(-5) = 0

p(-5) = (-5)3 + 2(-5)2 - 13(-5) + 10

= -125 + 50 + 65 + 10

= 0

So, (x + 5) is also a factor of p(x) = x3 + 2x2 - 13x + 10.

Answer 2

Answer:

$\huge \underbrace \green{★ Answer❀✿°᭄★}$

$let \: f(x) = {x}^{3} + 2 {x}^{2} - kx + 10$

$As \: ( x - 2)is \: the \: factor \: of \: f(x)$

$քutting(x - 2) = 0 \: ⇒ \: x = 2$

$⇒ \: f(2) = {2}^{3} + 2( {2})^{2} - k(2) + 10 \\ ⇒ \: 0 = 8 + 8 - 2k + 10$

$(as \: (x - 2) \: is \: a \: factor \: of \: f(x) \: ⇒ \: f(2) = 0)$

$⇒ \: 2k = 26 \\ \\ ⇒ \: \frac{26}{2} = 13(ans)$

$\huge \underline {Hope \: it \:Helps \: u}$