Question

find the value of a and b so that x-1 and x+2 are factors of f(x)=2x³+ax²+bx-14​

Answer 1

Answer:

If x - 1 is a factor..

then ;

x - 1 = 0

x = 1

p(1) = 2(1)^3 + a(1)^2 + b(1) - 14

0 = 2 + a + b - 14

a + b = 12

a = 12 - b -----(1)

x + 2 is a factor ...

then ;

x + 2 = 0

x = -2

p(-2) = 2 (-2)^3 + a(-2)^2 + b(-2) - 14

0 = -16 -4a -2b - 14

4a + 2b + 14 + 16 = 0

2a + b + 7 + 3 = 0

2a + b = -10 ----(2)

substituting eq(1) in eq(2)

2 (12 - b ) + b = -10

24 - 2b + b = -10

24 - b = - 10

b = 24 + 10

b = 34 ----(3)

substituting eq (3) in eq (1)

a = 12 - b

a = 12 - 34

a = -22

hope it helps