Nature of Roots

Explain the benefits of evaluating the discriminant of a quadratic equation before attempting to solve it. What does its values signifies?

Find the value of $k$ for the given quadratic equation, so it has equal roots.

$2x^2+kx+3=0$

Find the nature of the roots of the quadratic equations. if real roots exist, find them.

$2x^2-6x+3=0$

Find the nature of the roots of the quadratic equations. If the real roots exist, find them.

$3x^2-4\sqrt{3}x+4=0$

If the equation $x^2-bx+1=0$ does not possess real roots, then

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

Find the value of the discriminant of the quadratic equation $2x^2-4x+3=0$.

If graph of the quadratic equation lies above $x-$axis, then the nature of roots are;

Find the roots of $2x^2+2x+3=0$

Find the value of $k$ so that equation $x^2+5kx+16=0$ has no real roots.

Find the value of $k$ for which quadratic equation has real and distinct roots.
$x^2-kx+9=0$

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.
$x^2-2(k+1)x+k^2=0$