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Given-a-quadratic-function-f-x-3-4k-k-3-x-x-2-where-k-is-a-constant-is-always-negative-when-p-k-q-What-is-the-value-of-p-and-q-

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Question Number 136124 by bramlexs22 last updated on 18/Mar/21
Given a quadratic function f(x) =3-4k-(k+3) x-x^2, where k is a constant, is always negative when p<k<q. What is the value of p and q?
Given a quadratic function f(x) =3-4k-(k+3) x-x^2, where k is a constant, is always negative when p<k<q. What is the value of p and q?
Answered by EDWIN88 last updated on 18/Mar/21
f(x)=−x^2 −(k+3)x+3−4k < 0 ∀x∈R taking discriminant Δ<0 ∴ (k+3)^2 −4(−1)(3−4k)<0 k^2 +6k+9+12−16k<0 k^2 −10k+21<0 ⇒(k−7)(k−3)<0 we get 3 < k < 7 so { ((p=3)),((q=7)) :}
f(x)=−x2−(k+3)x+3−4k<0∀x∈RtakingdiscriminantΔ<0∴(k+3)2−4(−1)(3−4k)<0k2+6k+9+12−16k<0k2−10k+21<0⇒(k−7)(k−3)<0weget3<k<7so{p=3q=7

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