Find m, if the quadratic equation `(m-12)x^(2)+2(m-12)x+2=0` has real and eqaul roots.

find the values k for which the quadratic equation 2x^2 + Kx +3=0 has two real equal roots

If m is a number such that m le 5 , then the probability that quadratic equation 2x^(2) + 2mx + m + 1 = 0 has real roots is

The real roots of the quadratic equation x^(2)-x-1=0 are ___.

Find the discriminant of the quadratic equation 2x^(2)-4x+3=0 , and hence find the nature of its roots.

One of the roots of quadratic equation 2x^(2)+kx-2=0 is -2, find k.

Number of integral values of a such that the quadratic equation x^(2)+a x+a+1=0 has integral roots is

If alpha and beta are the roots of the quadratic equation x^(2) + sqrt(2) x + 3=0 form a quadratic equation with roots (1)/(alpha) and (1)/(beta)

If x=9 is one root of the quadratic equation x^(2)-11x+k=0 , then find the value of k.

If both the roots of the quadratic equation x^(2) -mx+4=0 are real and distinct and they lie in the interval [1,5] then m lies in the interval