The value of the discriminant $D$ of the quadratic equation $x^{2} + 5x + 1 = 0$ is $\ldots \ldots \ldots \ldots .$

The price of corn oil is ₹ $x$ per $kg$. If the price of corn oil is decreased by ₹ $10$ per $kg$,then how many kilograms of corn oil can be obtained for ₹ $500$ at the new rate?

Comparing the quadratic equation $5x^{2}-4x-1=0$ with the standard form $ax^{2}+bx+c=0$,we get $b=\ldots$

Find the roots of the quadratic equation using the quadratic formula:
$x^{2}-3 \sqrt{5} x+10=0$

Find a natural number whose square diminished by $84$ is equal to thrice of $8$ more than the given number.

Which of the following equations has no real roots?