Question

if K -2 is a factor of x cube + 9 X square + bx + 18 and a minus b is equal to 7 find the value of a and b​

Answer 1

Explanation:

Given

K-2 is a factor...

of

$f(x) = {x}^{3} + 9 {x}^{2} + bx + 18$

and

a-b = 7

By using factors theorem

$k - 2 \: \: is \: \: \: a \: \: factor \: \: then \\at \: \: k = 2 \: \: f(x) \: \: \: must \: \: be \: equal \: \: to \: \: zero$

$f(2) = {2}^{3} + 9( {2}^{2} ) + b(2) + 18 \\ 0 = 8 + 36 + 2b + 18 \\ 0 = 62 + 2b \\ 2b = - 62 \\ b = - 31$

$and \\ \\ a - b = 7 \\ a - ( - 31) = 7 \\ a + 31 = 7 \\ a = 7 - 31 \\ a = - 24$

a= -24

b = -31