Question 1187914
{{{2x^2 +3x-1=0 }}} are {{{alpha }}}and {{{beta}}}

find roots using quadratic formula

{{{x=(-b+-sqrt(b^2-4ac))/(2a) }}}......{{{a=2}}},{{{b=3, and {{{c=-1}}}

{{{x=(-3+-sqrt(3^2-4*2(-1)))/(2*2) }}}

{{{x=(-3+-sqrt(9+8))/4 }}}

{{{x=(-3+-sqrt(17))/4 }}}


=> {{{alpha =(-3+sqrt(17))/4 }}}  and {{{beta=(-3-sqrt(17))/4 }}}


Find the values of {{{alpha^2 -beta^2}}}:


{{{alpha^2 -beta^2=((-3+sqrt(17))/4 )^2-((-3-sqrt(17))/4 )^2}}}


{{{alpha^2 -beta^2=(-3+sqrt(17))^2/16 -(-3-sqrt(17))^2/16}}}


{{{alpha^2 -beta^2=(26 - 6 sqrt(17))/16 -(26 + 6 sqrt(17))/16}}}


{{{alpha^2 -beta^2=(26 - 6 sqrt(17) -26 - 6 sqrt(17))/16}}}


{{{alpha^2 -beta^2=( - 12 sqrt(17))/16}}}


{{{alpha^2 -beta^2=-(3sqrt(17))/4}}}