Question

For what value of K is x^2 - 2kx + 16 divisible by x+2
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Answer 1

${Sol}^{n} : \: \: \: \: \\ \\ = > f(x) = x + 2 = 0 \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 2$

Now, Putting the value of x in p(x) will result in zero as f(x) is factor of p(x).

$\: \: \: p(x) = > {x}^{2} - 2kx + 16 = 0 \\ p( - 2) = > {( - 2)}^{2} - 2k( - 2) + 16 = 0 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = > 4 + 4k + 16 = 0 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = > 4k = - 20 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = > k = - 5$

${ \huge{ \boxed{ \red{Value \: \: of \: \: k \: \: is \: -5}}}}$

$<marquee>MARK BRAINLIEST$

$<marquee>#Radhe_Radhe$