Question

Find the values for p and q so that 1 and -2 are the zeroes of the polynomial f (x)= x^3 + 10x^2 + px + q

Answer 1

Hey mate,

We know 1,-2 are zeroes then they must satisfy the equation,

Putting 1,

f (1) = 0

f (1) = 1 + 10 + p + q

0 = 11 + p + q ......1

Now putting -2

f (-2) = 0

0 = -8 + 40 - 2p + q

2p - q = 32....... 2

Solving 1 and 2 by adding,

3p = 21

p = 7

and putting p=7 in 1,

q = -18

hope this helps you out!