Question

(c) Find p and q such that 3 and - 1 are the zeros
of f(x) = x4 + px3 + x2 + 12x - 9.
​

Answer 1

Heyyyy,

x4 + 7x3 + 7x2 + px + q is exactly divisible by x2+ 7x + 12.

⇒ The remiander when x4 + 7x3 + 7x2 + px + q is divided by x2+ 7x + 12 is zero.

Remainder = (p - 35)x + (q + 60)

(p - 35) = 0

⇒ p = 35

(q + 60) = 0

⇒ q = -60

Hence, the values of p and q are 35 and -30.