The quadratic equation .............. has a root $x=3$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $16x^{2} - 40x + \frac{k-1}{2} = 0$.

Find the roots of the following quadratic equation by the method of completing the square: $5x^{2}-4x-10=0$

$16x^2 + 40x + k$ is a perfect square polynomial,then $k = \ldots$

$A$ car takes $60$ minutes less for a journey of $150\,km$,if its speed is increased by $5\,km/hr$ from its usual speed. Find the original speed of the car in $km/hr$.

Solve the following equation using the method of factorization and write its solution set: $4x^{2} + 4x = 15$.