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Question Number 132475 by Study last updated on 14/Feb/21

prove that x_1 +x_2 =−(b/a) x_1 and x_2 are roots of ax^2 +bx+c=0

provethatx1+x2=−bax1andx2arerootsofax2+bx+c=0

Commented by MJS_new last updated on 14/Feb/21

it′s just the solution formula again. solve the quadratic and add the solutions. where′s the problem?

it′sjustthesolutionformulaagain.solvethequadraticandaddthesolutions.where′stheproblem?

Commented by EDWIN88 last updated on 14/Feb/21

may be the problem why x_1 +x_2 =−(b/a)

maybetheproblemwhyx1+x2=−ba

Commented by MJS_new last updated on 14/Feb/21

as I said, solve by using the usual formula

asIsaid,solvebyusingtheusualformula

Commented by EDWIN88 last updated on 14/Feb/21

yes

yes

Answered by rs4089 last updated on 14/Feb/21

let x_1 and x_2 are roots of eq^n ax^2 +bx+c=0 we can writen as ax^2 +bx+c=a(x−x_1 )(x−x_1 ) compare cofficient of x both side... b=−a(x_1 +x_2 ) so x_1 +x_2 =((−b)/a)

letx1andx2arerootsofeqnax2+bx+c=0wecanwritenasax2+bx+c=a(x−x1)(x−x1)comparecofficientofxbothside...b=−a(x1+x2)sox1+x2=−ba

Answered by physicstutes last updated on 14/Feb/21

Or begin with the general solution to the quadratic: x = ((−b±(√(b^2 −4ac)))/(2a)) say, x_1 = ((−b+(√(b^2 −4ac)))/(2a)) and x_2 =((−b−(√(b^2 −4ac)))/(2a)) x_1 + x_2 = ((−b+(√(b^2 −4ac)))/(2a)) + ((−b−(√(b^2 −2ac)))/(2a)) = ((−b+(√(b^2 −4a4)) −b −(√(b^2 −4ac)))/(2a)) x_1 + x_2 = ((−b−b)/(2a)) = ((−b)/a) hence x_1 + x_2 =−(b/a) similarly it can be shown that x_1 x_2 = (c/a)

Orbeginwiththegeneralsolutiontothequadratic:x=−b±b2−4ac2asay,x1=−b+b2−4ac2aandx2=−b−b2−4ac2ax1+x2=−b+b2−4ac2a+−b−b2−2ac2a=−b+b2−4a4−b−b2−4ac2ax1+x2=−b−b2a=−bahencex1+x2=−basimilarlyitcanbeshownthatx1x2=ca

Commented by MJS_new last updated on 14/Feb/21

that′s exactly what I recommended if we answer the easiest questions, people wil never learn anything. you can do all their thinking − at least all their homework − for them for all eternity.

that′sexactlywhatIrecommendedifweanswertheeasiestquestions,peoplewilneverlearnanything.youcandoalltheirthinking−atleastalltheirhomework−forthemforalleternity.

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