Question

Let alpha and beta be two roots of the equation

Answer 1

Option 1 is correct

Taking a for alpha and b for beta we can write ,sum of roots =a+b =-2 and

product of roots ab=+2

Now a^3+b^3=(a+b)^3-3ab(a+b)

=(-2)^3-3×2(-2)=+8+12=4

a^2+b^2=(a+b)^2-2ab=(-2)^2-2×2=4-4=0

Now let a^3=c and b^3 =d

So cd=(a^3b^3)=(ab)^3=2^3=8

And c+d=4

Hence c^2+d^2=(c+d)^2-2cd

=(4)^2-2×8=0

 a^15+b^15

=c^5+d^5

=(c^3+d^3)((c^2+d^2)-c^2d^2(c+d)

=(c3+d^3)×0-(8)^2(4)=-256