Find the value of k in order that the roots of equation `3x^2-(1+4k)x+k^2+5=0` may be in the ratio of `3:1.`

Find the value of k for which the roots of the equation 3x^2-10x+k=0 are reciprocal of each other

If -2 is a root of the equation 3x^(2)+7x+p=0, find the value of k so that the roots of the equation x^(2)+k(4x+k-1)+p=0 are equal.

Find the values of k so that the quadratic equation x^(2)+2(k-1)x+k+5=0 has atleast one positive root

Find the values of k so that the quadratic equation x^(2)+2(k-1)x+k+5=0 has atleast one positive root.

Find the value of k for which the roots of the equation 3x^(2) - 10x + k = 0 are reciprocal of each other.

Find the value of K for which x=2 is a root of the equation 3x^(2)-2Kx+5=0 .

Find the value of k such that the equation (k - 12)x^2 - 2(k – 12)x + 2 = 0 may have equal roots.

If 3 is a root of the quadratic equation x^(2)-x+k=0 find the value of p so that the roots of the equation x^(2)+k(2x+k+2)+p=0 are equal.

For what value of k, -2 is a root of the equation 3x^(2)+4x+2k=0 ?

Find the value of k for which the quadratic equation (k+4)x^2+(k+1)x+1=0 has equal roots