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

Which of the following equations has two distinct real roots?

$A$ quadratic equation with integral coefficients must have integral roots. Justify your answer.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $2x^2 - 5x + 3 = 0$; $x = \frac{1}{2}$.

Values of $k$ for which the quadratic equation $2x^{2}-kx+k=0$ has equal roots is

$A$ two-digit number is such that the product of its digits is $6$. When $9$ is subtracted from the number,the resulting number is the number obtained by interchanging the digits. Find the original number.