Question

How do you solve the quadratic using the quadratic formula given `a^2-7a-10=0`?

Answer 1

`a = 7/2+-sqrt(89)/2`

Explanation:

The slight nuisance with this question is that the `a` used as a variable name clashes with the `a, b, c` that normally stand for the coefficients of the terms of a quadratic.

To sidestep this issue, consider the quadratic equation:

`x^2-7x-10 = 0`

This has the same zeros as our original quadratic, just expressed as values of `x` instead of values of `a`.

Our quadratic equation in `x` is of the form `ax^2+bx+c = 0` with `a=1`, `b=-7` and `c=-10`.

It therefore has zeros given by the quadratic formula:

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

`= (7+-sqrt((-7)^2-4(1)(-10)))/(2*1)`

`= (7+-sqrt(49+40))/2`

`= (7+-sqrt(89))/2`

`= 7/2+-sqrt(89)/2`

So the zeros of our original quadratic are given by:

`a = 7/2+-sqrt(89)/2`