Nature of Roots

If $x^2+x+2= 0$, find $x$.

Find the values of $k$ for which the quadratic equation $x^2+3x+k=0$ has no real roots.

Find the nature of the roots of the given equation: $x^2+2x+3=0$.

Find the value of $k$ for which the roots of the equation $\left(k+1\right)x^2+2\left(k+3\right)x+\left(k+8\right)=0$ are real and equal.

If the equation $k{x}^2-2kx+6=0$ has equal roots, then find the value of $k$.

If the equation $x^2-(k+4)x+2k+5=0$ has equal roots, find the value of $k$.

If $x=k$ is one of the solution of $2x^2+5x-k=0$, find the two possible values of $k$.

The nature of the roots for the following equations $4x^2-4x+1=0$ is real and _____.

Find the value of  $m$ for which the quadratic equation $(m-1)x^2+2(m+1)x+9=0$ has equal roots. 

If $-5$ is one root of quadratic equation $2x^2+px-15=0$ and roots of quadratic equation $p\left(x^2+x\right)+k=0$ is equal, then find the value of $k$.

If the roots of equation $x^2-kx+9=0$ are real and distinct, then $k>\_\_\_\_\_$.

Find the value of $k$ for which quadratic equation has real and distinct roots. Find the maximum integer value of $k$.
$k{x}^2+6x+1$

Find the value of $k$ for which quadratic equation has real and distinct roots.
$k{x}^2+2x+1=0$

Find the value of $k$ in the quadratic equation for which roots are real and equal.
$k{x}^2-5x+k=0$

Find the sum of values of $k$ in the quadratic equation for which roots are real and equal.
$(k+4)x^2+(k+1)x+1=0$

Find the sum of values of $k$ in the quadratic equation for which roots are real and equal.
$(k+1)x^2-2(k-1)x+1=0$

If the value of $k=m\sqrt{6}$ in the quadratic equation for which roots are real and equal, then find the value of $m$.
$2x^2+kx+3=0$

Find the value of $k$ in the quadratic equation for which roots are real and equal.
$x^2-2(k+1)x+k^2=0$

Find the value of $k$ in the quadratic equation for which roots are real and equal.
$kx(x-2)+6=0$

Find the positive value(s) of $k$, if the quadratic equation $3x^2-k\sqrt{3}x+4=0$ has equal roots.