if alpha and beta are the roots of 2x2+ x+3 =0, then equation whose roots are 1-alpha/1+alpha and 1-beta/1+beta is Share with your friends Share 0 Sanjay Kumar Manjhi answered this Dear Student,2x2+x+3=0Here, roots are α and β,Now we know that;α+β=-ba=-12.........(i)and,αβ=ca=32.......(ii)Now,The new quadratic equation has roots which are;1-α1+α and 1-β1+βNow, Summation of roots;1-α1+α+1-β1+β=(1+β)(1-α)+(1-β)(1+α)(1+α)(1+β)=1+β-α-αβ+1+α-β-αβ1+α+β+αβ=2(1-αβ)1+(α+β)+αβNow put value of (α+β) and αβ from (i) and (ii), we get;=2(1-32)1-12+32=-12Summation of roots of new quadratic equation =-12Now,(1-α1+α)×(1-β1+β)=1-α-β+αβ1+α+β+αβ=1-(α+β)+αβ1+(α+β)+αβNow put value of (α+β) and αβ from (i) and (ii), we get;=1+12+321-12+32=32Product of roots of new quadratic equation =32 We can write quadratic equation in the below mentioned form;x2-(sum of roots)x+(product of roots)=0So,⇒x2-(-12)x+32=0⇒2x2+x+3=0Which is identical as parent quadratic equation.Regards. 0 View Full Answer Dev answered this alpha + beta=-1/2 alphabeta=3/2 x2[1-alpha X 1- beta +1-b X 1+alpha/1= alphaX 1+beta and the whole term multiplied with 1-alpha X 1-beta/1+alpha X 1+beta =few simplification and then multiply because my answer was too long multiply on both sides by 2 and you will get 2x2-x +3=0 0
