The quadratic equation `x^(2)-9x+3=0` has roots `alpha and beta.If x^(2)-bx-c=0` has roots `alpha^(2)and beta^(2),` then `(b,c)` is

If alpha and beta are roots of the quadratic equation x ^(2) + 4x +3=0, then the equation whose roots are 2 alpha + beta and alpha + 2 beta is :

If the quadratic equation alpha x^2 +beta x+a^2+b^2+c^2-ab-bc-ca=0 has imaginary roots then

If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0, form a quadratic equation whose roots are alpha^(2)+beta^(2) and alpha^(-2) + beta^(-2) .

If alpha&beta are the roots of the quadratic equation a x^2+b x+c=0 , then the quadratic equation, a x^2-b x(x-1)+c(x-1)^2=0 has roots: alpha/(1-alpha),beta/(1-beta) (b) alpha-1,beta-1 alpha/(alpha+1),beta/(beta+1) (d) (1-alpha)/alpha,(1-beta)/beta

Consider a quadratic equation ax^2 + bx + c = 0 having roots alpha, beta . If 4a + 2b + c > 0,a-b+c 0 then |[alpha] + [beta]| can be {where [] is greatest integer}

If alphaandbeta be the roots of the quadratic equation x^(2)+px+q=0 , then find the quadratic equation whose roots are (alpha-beta)^(2)and(alpha+beta)^(2) .

The roots alpha and beta of the quadratic equation px^(2) + qx + r = 0 are real and of opposite signs. The roots of alpha(x-beta)^(2) + beta(x-alpha)^(2) = 0 are:

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

Let alpha and beta be the roots of the quadratic equation ax^(2)+bx+c=0, c ne 0, then form the quadratic equation whose roots are (1-alpha)/(alpha) and (1-beta)/(beta) .

If alpha, beta be the roots of quadratic equation ax^(2)+bx+c=0 , then find the value of (a alpha^(2)+c)/(a alpha+b)+(a beta^(2)+c)/(a beta+b) ?