Prove that `tanpi/(10)` is a root of polynomial equation `5x^4-10 x^2+1=0.`

If tan^-1y=5tan^-1, x express as an algebraic function of x and hence show that tan 18^0 is a root of the equation 5u^4 -10u^2 +1=0

The number of real roots of the polynomial equation x^(4)-x^(2)+2x-1=0 is

Prove that sinfrac {pi}{14} is a root of the equation 8x^(3) -4x^(2) - 4x +1 = 0 .

Real roots of equation x^(2)+5|x|+4=0 are

Roots of equation x^(4)-10x^(3)+26x^(2)-10x+1=0 are

Sum of the roots of the equation x^2 +7x+10=0

The roots of the equation x^(2) + 5x + 1 = 0 are

Find the roots common to the equations x^5-x^3+x^2-1=0 and x^4= 1 .

Prove that x=2 and x=3 are roots of the equation :det[[x-5,32,x]]=0