For each pair of numbers find the values of a, b, and c for which the quadratic equation

Question

ax^2 + bx + c = 0 has the solutions -5 and 2.?

Answer 1

Quadratic equation ax² + bx + c = 0

The quadratic equation have two roots.

From Factor theorem,

When f(c) = 0 then x - c is a factor of a polynomial.

- 5 and 2 are roots of ax² + bx + c = 0

So (x + 5)(x - 2) = 0

x(x) + x(- 2) + 5(x) + 5(- 2) = 0

x² - 2x + 5x - 10 = 0

x² + 3x - 10 = 0

Compare it to ax² + bx + c = 0.

The values : a = 1, b = 3 and c = - 10.