Poly-Q5.md

Find the sum of the squares of the roots of the polynomial $x^4 - 3x^3 + 12x^2 - x +15 =0$

Application of Viete's formula and cancellation of resulting squares

This video from Khan Academy https://www.youtube.com/watch?v=bbeWLtarzrE is useful for the technique.

Once you have followed the video's logic the answer is quite simple. For a polynomial of degree n

The sum of the squares of the roots is found by $a_1^2 - 2a_2$

For our equation $a_1 = -3$ and $a_2 = 12$

So the answer is $9-24= -15$ remember, as mentioned in the video, polynomials can have imaginary numbers as roots which is how the sum of the squares of the roots can be negative.