Question

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

Answer 1

If alpha,beta are the roots of 2x^2+x+3=0 then

alpha+beta=-b/a=-1/2

alpha beta=c/a=3/2

now,

we need quatratic equation whose roots are

1-alpha/1+alpha. and 1-beta/1+beta

so,

x^2-[(1-alpha/1+alpha)+(1-beta/1+beta)]x+[( 1-alpha/1+alpha) (1-beta/1+beta)]=0

x^2-{[1-alpha+beta-alpha beta+1-beta+alpha-alpha beta]/1+alpha+beta+alpha beta}x+[1-alpha-beta+alpha beta]/[1+alpha+beta+ alpha beta]=0

x^2-[ (2-3/2)/(1-1/2+3/2) ]x+[(1-(-1/2)+3/2)/1-1/2+3/2)]=0

x^2-[1/2/2]x+[3/2]=0.

x^2-1/4x+3/2=0

4x^2-x+6=0

This is required quadratic equation with given roots


Hope this really helps you!!! If so please mark me!!!

Answer 2

Answer:

hi everyone the answer is 2x²-x+3......if you any doubts message me or ask me in comments..i think my solution may help you.