Question

find a and b so that (x+1) and (x-3) are factors of x^3+ax^2+bx-12​

Answer 1

Answer:

Here,

Let f(x) = x³+ax² +bx -12

Comparing (x+1) with (x-k), k= - 1

Using factor theorem,

f(-1) = 0

or, (-1)³ +a(-1)² +b(-1) -12 = 0

or, -1 +a -b -12 = 0

or, a-b = 13.............(1)

Again,

Comparing (x-3) with (x-k), k = 3

Using factor theorem,

f(3) = 0

or, 3³ +a(3)² +b×3 - 12 = 0

or, 27 + 9a +3b -12= 0

or, 9a+3b = -15...............(2)

Solving (1) and (2),

a= 2 and b = -11

Step-by-step explanation: