Question

if (x-2) and ( x+3) are factor of x3 + ax2 +bx -30, find a and b​

Answer 1

Step-by-step explanation:

If ab = 0 and a × b = ab

then either a or b equals to 0.

x-2 = 0

=》x = 2

Putting this value in the equation we get

2³ + 2²a + 2b - 30 = 0

=》 8 +4a+2b-30 = 0

=》 4a+2b = 22

= 》 2a+b = 11 ................................Eq (1)

or

x+3 = 0

=》 x = -3

(-3)³ + (-3)²a + (-3)b -30 = 0

=》-27 + 9a - 3b - 30 = 0

=》 9a - 3b = 57

=》 3a - b = 19 ...............................Eq (2)

Eq (1) + Eq (2) gives

5a = 30

=》 a = 6

putting the value of a in Eq (1) we get

2×6+b = 11

=》b = 11 - 12 = -1