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Question Number 215168 by MathematicalUser2357 last updated on 30/Dec/24

Let two roots of the equation x^2 +2mx+m^2 −2m+3=0 is α, β(For α<β), (2) Find (α−β)^2 Using m. (3) If β−α=2, Solve for m. If you don′t solve it, I will force you to solve.

Lettworootsoftheequationx2+2mx+m2−2m+3=0isα,β(Forα<β),(2)Find(α−β)2Usingm.(3)Ifβ−α=2,Solveform.Ifyoudon′tsolveit,Iwillforceyoutosolve.

Answered by A5T last updated on 30/Dec/24

α+β=−2m; αβ=m^2 −2m+3 (α−β)^2 =(α+β)^2 −4αβ=8m−12 β−α=2⇒(α−β)^2 =4=8m−12⇒m=2

α+β=−2m;αβ=m2−2m+3(α−β)2=(α+β)2−4αβ=8m−12β−α=2⇒(α−β)2=4=8m−12⇒m=2

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