Question

P(x) = x⁴ + ax³ + bx² + cx+ d and p(1) = p(2) = p(3) =0 then find the value of p(4) + p(0).

Answer 1

p(x) = x⁴ + a x³+b x² + c x + d

If p(1) = p(2) = p(3) = 0, it means that (x-1) , (x-2) , (x-3) are factors of P(x). Let the last factor of P(x) be (x - m). Hence

p(x) = x⁴ + a x³+b x² + c x + d = (x-1) (x - 2 ) ( x - 3 ) (x - m)

comparing the constant term = d = 6m => m = d/6

p(4) + p(0) = 3 * 2 * 1 * (4 - m) + (-1 * -2 * -3 * -m)
= 24 - 6 m + 6m = 24

Answer is 24