Question

if x=2 and x=5 are roots of px^2-7x+5f=0, find the value of p and f

Answer 1

If 2 and 5 are solutions to the polynomial, the polynomial must be divisible by

(x - 2) and (x - 5). Since it's a quadratic, the polynomial must then be

a(x - 2)(x - 5)

Where "a" is some constant. Expanding, we get:

a(x - 2)(x - 5) = ax^2 -7ax + 10a

This is supposed to be equivalent to the original:

ax^2 -7ax + 10a = px^2 - 7x + 5f

From this, it becomes obvious that a = 1, p = 1, and f = 2.