Question

How do I solve w(w)-24w+144=0 for the polynomial roots?

Answer 1

The roots of the equation are the x-intercepts. What we are being asked is to find the values of these x intercepts for this quadratic equation (which can have 0, 1 or 2 roots depending on the parabola position).
So,
w^2 - 24w + 144 = 0
We can use factoring a perfect trinomial. We want to look numbers that multiply to 144 that add up to 12 (this can include negative numbers).
(w -12)(w -12) ---- these are the factors and since we are asked to solve we must find the respective solutions. But, since these are the same factors, we only need to solve for one.
w - 12 = 0
w = 12 ---- ANSWER

To double check plug 12 for w into the original equation and see if the LHS = RHS or 0 = 0.

Answer 2

Sorry I meant to the two numbers that multiply to 144 that add up to -24. My bad :)