help!!!

Question

If the roots of an equation are 5 and -9, then write the equation in quadratic form. This means write the equation in form of y=ax^2 + bx + c.

Answer 1

The roots of the equation are 5 and  - 9

The quadratic equation y = ax^2 + bx + c have two roots.

From the factor therom ,

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

So the (x - 5) and (x + 9) are factors of required quadratic equation.

(x - 5)(x + 9) = x(x) + x(9) - 5(x) - 5(9)

= x² + 9x - 5x - 45

= x² + 4x - 45

Required equation y = x² + 4x - 45.