Please help! 20 points available! Will give brainliest!

The solutions to
\[x^2 + 5x + 3 = 0\]are $p$ and $q,$ and the solutions to
\[x^2 + bx + c = 0\]are $p^2$ and $q^2.$
Find $b + c.$

-10

Step-by-step explanation:

x² + 5x + 3 = 0

x² - (sum of roots)x + product = p

p + q = -5

pq = 3

(p + q)² = (-5)²

p² + 2pq + q² = 25

p² + q² = 25 - 2(3)

p² + q² = 19

p²q² = (pq)² = 3² = 9

x² - (19)x + 9

x² - 19x + 9

x² + bx + c

b = -19

c = 9

b + c = -19 + 9 = -10

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