Question

What is the quadratic equation?

`3x^2-5x-12`

Answer 1

If `3x^2-5x-12 =0`
then `x=-4/3 or 3`

Explanation:

`f(x) = 3x^2-5x-12`

First note that this is not an equation. It is a second degree polynomial in `x` with real coefficients, often referred to as a quadratic function.

If we seek to find the roots of `f(x)` then this does lead to a quadratic equation where `f(x) = 0`. The roots will be the two values of `x` that satisfy this equation. These roots can be real or complex and can also be coincident.

Let's find the roots of `f(x)`:

We set `f(x) =0`

`:. 3x^2-5x-12 =0`

Which factorises to:

`(3x+4)(x-3) =0`

Hence, either `(3x+4)=0 or (x-3)=0`

`:. x=-4/3 or 3`