Question

Find a quadratic equation whose roots are (7,-5)?write in standard form

Answer 1

`x^2-2x-35`

Explanation:

A quadratic function in standard form is written: `ax^2+bx+c`, where `a, b and c` are real coefficients.

Let our quadratic function be `f(x)`

The roots of `f(x)` are those values of `x` for which `f(x)=0`

Here we are told that `+7 and -5` are roots.

This implies that `(x-7) and (x+5)` are factors of `f(x)`

Hence, `f(x) = (x-7)(x+5)`

`:. f(x) = x^2-2x-35`