Question

The sides of a triangle are in the ratio $1:\sqrt{3}:2$. Then the angles are in the ratio

• A. 6
• B. 3
• C. 6i
• D. 3i

Answer 1

Answer: (A)

We have,
$(x-1{)}^3+64=0$
$\Rightarrow (x-1{)}^3=-64$
$\Rightarrow (x-1{)}^3=(-4{)}^3$
$\Rightarrow x-1=-4,-4w,-4w^2$
$\Rightarrow X=-3,-4w+1,-4w^2+1$
Complex roots of the equations are
$-4w+1,-4w^2+1$
Sum of complex roots are
$-4w+1-4w^2+1=-4\left(w+w^2\right)+2$
$=-4(-1)+2=4+2=6[\because 1+w+w^2=0]$