Question

if (x-2)and(x+3)are factors of x^3+ax+bx-30, find a and b​

Answer 1

$Let \:p(x) = x^{3} + ax+bx-30$

$i) (x+2) \:is \:a \: factor \:p(x) \:then \: p(-2) = 0$

$\implies (-2)^{3} + a(-2) + b(-2) - 30 =0$

$\implies -8 -2a -2b - 30 =0$

/* divide each term by 2 , we get */

$\implies -4 - a - b - 15 = 0$

$\implies a + b = 19\: --(1)$

$i) (x+3) \:is \:a \: factor \:p(x) \:then \: p(-3) = 0$

$\implies (-3)^{3} + a(-3) + b(-3) - 30 =0$

$\implies -27 -3a -3b - 30 =0$

/* divide each term by 3 , we get */

$\implies -9 - a - b - 10 = 0$

$\implies a + b = 19\: --(2)$

$Here , (1) = (2)$

$For \: all \: real \: values \: a \:and \: b \: which \\satisify \: the \: equation \: are \: solutions$

$a , \: b \:have \: infinitely \:many \: solutions$

•••♪

Answer 2

Hopes helps you friend plz mark it's as brainliest answer ..