Question

If f (x) is a quadratic polynomial, such that f (5) = 35 and 1(-5) = 15, and f(p) = f(0) = 0, find p + q.
-3
5
o
Cannot be determined​

Answer 1

Answer:

f(p) = f(q) = 0 so p & q are zeros of polynomial.

Quadratic is

$(x - p)(x - q) = 0$

${x}^{2} - (p + q)x + pq = 0$

now, f(5) = 35

so.

${5}^{2} - (p + q) \times 5 + pq = 35$

$- 5(p + q) + pq = 10..........(i)$

also. f(-5) = 15

so,

$( - 5) {}^{2} + 5(p + q) + pq = 15$

$5(p + q) + pq = - 10...........(ii)$

apply (ii) - (i),. we get

$10(p + q) = - 20$

$p + q = - 2$

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