Q 2 Ex 4.2 Ch-4 Quadratic equations

If alpha and beta are the roots of a quadratic equation such that alpha+beta=2, alpha^4+beta^4=272 , then the quadratic equation is

Let p, q in R . If 2- sqrt3 is a root of the quadratic equation, x^(2)+px+q=0, then

If-4 is a root of the quadratic equation x^2+p x-4=0 and the quadratic equation x^2+p x+k=0 has equal roots, find the value of kdot

If alpha != beta but, alpha^(2) = 4alpha - 2 and beta^(2) = 4beta - 2 then the quadratic equation with roots (alpha)/(beta) and (beta)/(alpha) is

Find the roots of the quadratic equations by applying the quadratic formula. (i) 2x^2 -7x+3 =0 (ii) 2x^2+x-4 =0 (iii) 4x^2+4sqrt3x+3=0 (iv) 2x^2+x+4 = 0

If 2 is a root of the quadratic equation 3x^2+p x-8=0 and the quadratic equation 4x^2-2p x+k=0 has equal roots, find the value of kdot

If 2 is a root of the equation x^2+a x+12=0 and the quadratic equation x^2+a x+q=0 has equal roots, then q= (a) 12 (b) 8 (c) 20 (d) 16

Find the value(s) of k so that, the quadratic equation x^2 - 4kx + k = 0 has equal roots.

Find the roots of the quadratic equations (if they exist) by the method of completing the square. 4x^2+4sqrt(3)x+3=0