The roots of the cubic equation (z + `alpha` `beta`)^3 = `alpha`^3 , `alpha` is not equal to 0, represent the vertices of a triangle of sides of length

The roots of the equation x^(2)+6x-4=0 are alpha, beta . Find the quadratic equation whose roots area (alpha^(2)beta) and beta^(2)alpha

If alpha+beta=4" and "alpha^(3)+beta^(3)=44" the "alpha, beta are the roots of the equation

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

In a quadratic equation with roots alpha and beta where alpha+beta=-4 and alpha beta=-1 , then required equation is ……………

If the angles alpha, beta, gamma of a triangle satisfy the relation, sin((alpha-beta)/(2)) + sin ((alpha -gamma)/(2)) + sin((3alpha)/(2)) = (3)/(2) , then The measure of the smallest angle of the triangle is

Given that alpha , gamma are roots of the equation Ax^(2)-4x+1=0 and beta , delta are roots of the equation Bx^(2)-6x+1=0 . If alpha , beta , gamma and delta are in H.P. , then

The roots of the equation 2x^(2)-7x+5=0 are alpha and beta . Without solving the root find (alpha)/(beta)+(beta)/(alpha)