x(x-3)=4,has two roots `alpha`and `beta`then `alpha^2+beta^2=?`

If the equation 2x^(4)+x^(3)-2x-1=0 has two real roots alpha and beta , then between alpha and beta the equation 8x^(3)+3x^(2)-2=0 has -

If (alpha,beta) ∈ R are two of an quadratic equations,then the equation will be given as x^2-(alpha+beta)x+alphabeta =0 If for a quadratic equation,the roots alpha,beta satisfy alpha^2+beta^2 =5, 3(alpha^5+beta^5)=11(alpha^3+beta^3) ,then the equations will be

The roots of the equation x^2+3x+4=0 are alpha and beta .Form the equations whose roots are (alpha+beta)^2 and (alpha-beta)^2

-alpha^2/beta and -beta^2/alpha are the roots of the equation 3x^2-18x+2=0 . Find the equation whose roots are alpha and beta ( alpha,beta real).

Two roots of 5x^2 + 7x + 3 = 0 are alpha and beta . The value of (alpha^3 + beta^3)/(alpha^-1 + beta^-1) is_____

Roots of the equation 3x^2 -6x+4=0 are alpha and beta then find the value of alpha^3 +beta^3

If alpha ,beta are the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0 then find the equation whose roots are (alpha + beta)^2 and (alpha-beta)^2

Suppose that the equation f(x)=x^(2)+bx+c=0 has two distinct real roots alpha and beta . The angle between the tangent to the curve y=f(x) at the point ((alpha+beta)/(2),f((alpha+beta)/(2))) and the positive direction of the x -axis is-

If f(x)=(x-1)(x-2)(x-3)(x-4) , show that the equation f'(x)=0 has three roots alpha, beta and gamma where 1 lt alpha lt 2, 2 lt beta lt 3 and 3 lt gamma lt 4 .

IF alpha and beta be the roots of the equation x^2+3x+4=0 , find the equation whose roots are (alpha+beta)^2 and (alpha+beta)^2