If the equation `x^2 + y^2-10x + 21 = 0` has real roots `x=alpha and y =beta` then

If the equation x^(2)+y^(2)-10x+21=0 has real roots x=alphaandy=beta then

If the equation 3x^(2) - 2x-3 = 0 has roots alpha , and beta then alpha.beta = "______" .

If alpha and beta are the roots of the equation x^2 +x+1 = 0 , the equation whose roots are alpha^19 and beta^7 is

If alpha and beta are the roots of the equation x^2 - 10x + 5 = 0 , then equation whose roots are (alpha+beta)^2 and (alpha-beta)^2 is

If alpha and beta are roots of the equation x^2 – x-1 = 0 , then the equation where roots are alpha/beta and beta/alpha is:

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

-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).

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 alpha and beta be the roots of the equation x^(2) + 7x + 12 = 0 . Then equation whose roots are (alpha + beta)^(2) and (alpha - beta)^(2) is :