Question

I urgently need help with a quadratic equations problem it is due tonight! The roots of x^2 + 5x + 3 = 0 are p and q, and the roots of x^2 + bx + c = 0 are p^2 and q^2. Find b + c. False answers will be reported. I REALLY REALLY need an answer!! PLEAAASE!

Answer 1

Answer:

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Answer 2

For any quadratic equation of the form ax² + bx + c = 0, if their roots are α and β, we know that

Sum of roots, α+β = -b/a

Product of roots, αβ = c/a

Let f(x) = x² + 5x + 3 = 0

Sum of roots, p + q = -5

Product of roots, pq = 3

p + q = -5

(p + q)² = 25

p² + q² + 2pq = 25

p² + q²  + 2×3 = 25

p² + q² = 25 - 6

$\huge\black\boxed{p^2+q^2 = 19}$

Let g(x) = x² + bx + c = 0

Sum of roots, p² + q² = -b

Product of roots, p²q² = c

But p² + q² = 19

So ,-b = 19

b = -19

p²q² = c

(pq)² = c

3² = c

c = 9

SO

b+c = -10