If x-1 and x+3 are the factors of x3+10x2+ax+b find a and b

llm

Answered on Thu Mar 31 2022

We have,

F(x)= x³+10x²+ax+b

Now, x-1 and x+3 are the factors of F(x), that means for x =1 and x = -3 F(x) =0

So, F(1) = 1³ + 10(1)² + a(1) + b

0 = 1 + 10 + a + b

a + b = -11 ….(1)

Now,

F(-3) = -3³ + 10(-3)² + a(-3) +b

0 = -27 + 10(9) -3a + b

0 = -27 + 90 -3a + b

3a - b = 63 ….(2)

Adding equation 1 and 2, we get

a + b + 3a - b= -11 + 63

4a = 52

a = 52/4

a = 13

Now, putting value of a in equation 1, we, get

13 + b = -11

b = -11 -13

b = -24

Thus, value of a and b are 13 and -24 respectively.