Question

If two zeros of a quadratic polynomial are 0,0 then the corresponding polynomial is of the form (a, b, are non-zero Real numbers )

Answer 1

If the zeroes are at x = 4 and at x = –5, then, subtracting, the factor equations were x – 4 = 0 and x – (–5) = x + 5 = 0. Then the factors were x – 4 and x + 5 . Any factorable quadratic is going to have just the two factors, so these must be them. Then the original quadratic was something like:

(x – 4)(x + 5) = x2 – 4x + 5x – 20 = x2 + x – 20