Question

find the value of a when g(x) is a factor of p(x).



1. g(x) =x+1; p(x)=x power 2 +ax+2.​

Answer 1

here , g(x) = x + 1

=> x + 1 = 0

=> x = -1

if g(x) is a factor of P(x) , then

p(-1) = 0

p(x) = x² + ax + 2

=> p(-1) = (-1)² + a(-1) + 2

=> 0 = 1 + 2 - a

=> a = 3

The value of a is 3 .

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Answer 2

find the value of a , when g(x) is a factor of p(x).

1. g(x) =x+1;
$p(x) = {x}^{2} + ax + 2$
As we know that if g(x) is a factor polynomial of p(x) then by factor theorem it must satisfies the polynomial p(x).

Calculate value of x,by g(x)

$g(x) = x + 1 \\ \\ x + 1 = 0 \\ \\ x = - 1$
Find P(-1)

$p( - 1) = 0\\ \\ p( - 1) = ( { - 1)}^{2} + a(-1) + 2 \\ \\ 1 - a + 2 = 0 \\ \\ -a + 3 = 0 \\ \\ -a = - 3 \\ \\a=3$
Hope it helps you