Nature of Roots of a Quadratic Equation

In the quadratic equation $k{x}^2-6x-1=0$, determine the values of $k$ for which the equation does not have real roots.

Determine the value(s) of $p$ for which quadratic equation $2x^2+3x+p=0$ has real roots.

If $-2$ is a root of the quadratic equation $3x^2+7x+p=0$, find the values of $k$ for which the roots of the equation $x^2+k\left(4x+k-1\right)+p=0$ are equal.

Find the non-zero value of $k$, for which the quadratic equation $\left(3k+1\right)x^2+2\left(k+1\right)x+1=0$ has equal roots. Hence, find the roots of the equation.

Find the value(s) of $k$ for which following equation has equal roots: $x^2+k\left(2x+k-1\right)+2=0$

Find the value(s) of $k$ for which following equation has equal roots: $kx\left(x-2\sqrt{5}\right)+10=0$

Find the value(s) of $k$ for which following equation has equal roots: $kx\left(3x+10\right)+25=0$

Find the value(s) of $k$ for which following equation has equal roots: $kx\left(x-3\right)+9=0$

Find the value(s) of $k$ for which given equation has equal roots: $\left(k-12\right)x^2+2\left(k-12\right)x+2=0$

Find the value(s) of $k$ for which given equation has equal roots: $y^2+k^2=2\left(k+1\right)y$

Find the value(s) of $k$ for which given equation has equal roots: $9x^2-3kx+k=0$

Find the value(s) of $k$ for which given equation has equal roots: $4x^2+kx+3=0$

Find whether the equation has real roots; if real roots exist, find them: $-2x^2+3x+2=0$

Find whether the equation has real roots; if real roots exist, find them: $8x^2+2x-3=0$

Find the values of $k$ for which $kx\left(5x-6\right)+9=0$ has two equal roots.

Find the values of $k$ for which $x^2-2\left(1+3k\right)x+7\left(3+2k\right)=0$ has two equal roots.

Find the values of $k$ for which $\left(k-4\right)x^2+2\left(k-4\right)x+4=0$ has two equal roots.

Find the values of $k$ for which $k^2{x}^2-2\left(2k-1\right)x+4=0$ has equal roots.

Find the roots of $2x^2-3x+5=0$ using the quadratic formula if the roots exist.

Find the discriminant of the equation and hence find the nature of the roots. Also, find them if they are real: $4x^2+7x+2=0$