# How do you find the roots, real and imaginary, of #y= 2 (x + 1) (x - 4) # using the quadratic formula?

##### 2 Answers

#### Explanation:

You don't need a quadratic formula for this, since it is in the factored form, you just need to set each expression in the brackets equal to zero, and then find the roots.

#### Explanation:

As we are instructed to use the formula it is perhaps better to change the given equation into the format of

Not only that, I suspect that part of the agenda of this question is to see if you can 'handle' expansion of brackets.

Multiplying everything inside the right brackets by everything in the left.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thus we have;

So

As the content of the root (determinate) is not negative there are no imaginary roots. That is, in this case, the graph crosses the axis.

Note: if the determinate is 0 then the x-axis is tangential to the max/min