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