If alpha and beta are the roots of 2x²+7x-2=0 without solving form an equation whose roots are alpha squared and beta squared?

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Answer 1 · 2018-01-09T08:29:12

The equation is #4x^2-57x+4=0#

The quadratic equation is

#2x^2+7x-2=0#

Rewriting the equation as

#x^2+7/2x-1=0#

If the roots of the equation are #alpha# and #beta#

Then

#alpha+beta=-7/2#

and #alphabeta=-1#

#alpha^2+beta^2=(alpha+beta)^2-2alphabeta=49/4+2=57/4#

#alpha^2beta^2=(-1)^2=1#

The equation with roots #alpha^2# and #beta^2# is

#x^2-57/4x+1=0#

#4x^2-57x+4=0#