Question

How do you find the roots, real and imaginary, of `y= 5x^2 - 2x-45` using the quadratic formula?

Answer 1

Since `b^2-4ac` is 904 which is a positive number, the given quadratic equation has real roots.

`x=(2+-sqrt904)/10`

Explanation:

When the quadratic equation is in the form -

`ax^2+bx+c=0`

Then its roots are given by

`x=(-b+-sqrt(b^2-(4ac)))/(2a)`

In this `b^2-4ac` determines whether a given equation has real roots or imaginary roots.

If `b^2-4ac` is positive the roots are positive.

If `b^2-4ac` is negative the roots are negative.

In our case -

`(-2)^2-(4xx5xx-45)`
`4 - (-900)`
`4+900=904`

Since `b^2-4ac` is 904 which is a positive number, the given quadratic equation has real roots. So we should be able to plug into the quadratic formula without having imaginary numbers:

`x=(2+-sqrt(904))/(2(5))`

`x=(2+-sqrt904)/10`