Find a polynomial function of least degree with real coefficients satisfying the given properties.

Question

zeros -3, 0, and 4

f(1) =10

Answer 1

if zeros are -3, 0, 4, it could be

f(x) = x(x+3)(x-4)

but (1,10) lies on it , so we have to stretch it to pass through that point without wrecking the zeros

f(x) = ax(x+3)(x-4)

10 = a(4)(-3)
-12a = 10
a = -5/6

f(x) = -(5/6)x(x+3)(x-4)

Answer 2

Thank you.