Prove that the roots of the equation `x^4-2x^2+4=0` forms a rectangle.

If t_1a n dt_2 are the ends of a focal chord of the parabola y^2=4a x , then prove that the roots of the equation t_1x^2+a x+t_2=0 are real.

Find the values of a for which all the roots of the equation x^4-4x^3-8x^2+a=0 are real.

It is known that the roots of the equation x^3-6x^2-4x+24=0 are in arithmetic progression. Find its roots.

If alpha and beta are the roots of the equation 3x^(2) - 4x+1=0 form a quadratic equation whose roots are (alpha^2)/(beta) and beta^(2)alpha .

Find the roots of the equation x^2+sqrt(3) x+3/4

Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0 cannot be different, if real.

Find how many roots of the equations x^4+2x^2-8x+3=0.

If alpha, beta and gamma are the roots of the cubic equation x^3 + 2x^2 + 3x + 4 = 0, for a cubic equation roots are 2 alpha, 2 beta, 2 gamma

If alpha, beta and gamma are the roots of the cubic equation x^3 + 2x^2 + 3x + 4 = 0, for a cubic equation roots are 1/alpha, 1/beta, 1/gamma

If alpha, beta and gamma are the roots of the cubic equation x^3 + 2x^2 + 3x + 4 = 0, for a cubic equation roots are -alpha, -beta, -gamma