The function f : x \(\to\) x\(^2\) + px + q has turning point when x = -3 and remainder of -6 when divided by (x + 2). Find the value of q.
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Correct Answer: Option B
Explanation:
f (x) = x\(^2\) + px + q
\(\frac{dy}{dx}\) = 2x + p
2x + p = 0
2(-3) + p = 0
p = +6
f(-2) = -2\(^2\) + p(-2) + q
= -6 2p + q = -10
-2(-16) + q = -10
-12 + q = -10
q = -10 + 12
= 2
f (x) = x\(^2\) + px + q
\(\frac{dy}{dx}\) = 2x + p
2x + p = 0
2(-3) + p = 0
p = +6
f(-2) = -2\(^2\) + p(-2) + q
= -6 2p + q = -10
-2(-16) + q = -10
-12 + q = -10
q = -10 + 12
= 2