Answer:
p² -2q
Step-by-step explanation:
A quadratic with roots "a" and "b" can be written as ...
(x -a)(x -b) = 0 = x² -(a+b)x +ab
Comparing this to the given equation, we find the relationship between p and q and the roots to be ...
p = -(a+b)
q = ab
If we square p we have a number that includes the sum of the squares of the roots:
p² = (-(a+b))² = a² +2ab +b²
We can get rid of the 2ab term in this by making use of q:
p² - 2q = a² +2ab + b² -2ab = a² +b² . . . . the desired sum
