Question

find the value of A and B so that 2 x cube + x square + X + b has X + 2 and 2x - 1 as factors​

Answer 1

Answer:

Polynomial , x -ax -13x + b has two factors (x-1) and (x +3)

it means, x = 1 and -3 are the roots (zeros ) of x° -ax2 -13x + b.

so,

put x = 1 in polynomial .

(1) 3 -a (1)2 -13(1) + b = 0

1 - a -13 + b = 0

-a + b = 12 --(1)

put x = -3

(-3)* -a(-3)2 -13(-3) + b = 0

-27 -9a +39 + b = 0

-9a + b = -12 -(2)

subtract equation (1) and (2)

-a + b + 9a - b = 12 + 12

8a = 24

a= 3

put a = 3 in equation (1)

b = 15