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Given-P-x-x-4-2x-3-41x-2-42x-360-Determinate-Q-x-a-quadratic-poly-nom-such-that-P-x-Q-x-2-42-Q-x-360-

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Question Number 104181 by mathocean1 last updated on 19/Jul/20
Given P(x)=x^4 +2x^3 −41x^2 +42x+360 Determinate Q(x) a quadratic poly− nom such that: P(x)=(Q(x))^2 −42(Q(x))+360
GivenP(x)=x4+2x3−41x2+42x+360DeterminateQ(x)aquadraticpoly−nomsuchthat:P(x)=(Q(x))2−42(Q(x))+360
Answered by mr W last updated on 19/Jul/20
let Q(x)=x^2 +bx+c P(x)=(Q(x))^2 −42(Q(x))+360 =x^4 +2bx^3 +(b^2 +2c)x^2 +2bcx+c^2 −42x^2 −42x−42c+360 ⇒c^2 −42c+360=360 ⇒c=42 ⇒2bc−42=42 ⇒bc=42 ⇒b=1 ⇒b^2 +2c−42=41=41 ok! ⇒2b=2=2 ok! ⇒Q(x)=x^2 +x+42
letQ(x)=x2+bx+cP(x)=(Q(x))2−42(Q(x))+360=x4+2bx3+(b2+2c)x2+2bcx+c2−42x2−42x−42c+360⇒c2−42c+360=360⇒c=42⇒2bc−42=42⇒bc=42⇒b=1⇒b2+2c−42=41=41ok!⇒2b=2=2ok!⇒Q(x)=x2+x+42
Commented by mathocean1 last updated on 19/Jul/20
thank you sir!
thankyousir!
Commented by mathocean1 last updated on 19/Jul/20
sir can we also admit that the general form for quadratic polynoms is Q(x)=ax^2 +bx+c ?
sircanwealsoadmitthatthegeneralformforquadraticpolynomsisQ(x)=ax2+bx+c?
Commented by mr W last updated on 19/Jul/20
yes, but here it′s obvious that a=1.
yes,buthereit′sobviousthata=1.

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