Question

f(x)=px^2+qx-5. f(-1) and f(1)=-9

(a)find the values of p and q

(b)the values of x for which f(x)=1.

Answer 1

f(-1) = -9 = p(-1)^2 + q(-1) - 5 = p - q - 5
f(1) = -9 = p(1)^2 + q(1) - 5 = p + q - 5

therefore p - q - 5 = p + q - 5 = -9

p - q - 5 = -9
p + q - 5 = -9
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2p - 10 = -18
2p = -8
p = -4
-4 -q -5 = -9
q = 0

Checking our work, -4(-1)^2 + 0(-1) - 5 = -9

for part b, we need to set f(x) = 1 = px^2 + qx -5
1 = -4x^2 + 0x - 5
0 = -4x^2 + 0x - 6
use the quadratic formula to solve for x