M L Aggarwal Solutions for Exercise 4: Exercise 5.4

Find the value(s) of $k$ for which the following quadratic equation has equal roots:

$\left(k-4\right)x^2+2\left(k-4\right)x+4=0$.

Find the value(s) of $m$ for which the following quadratic equation has real and equal roots:

$x^2+2\left(m-1\right)x+\left(m+5\right)=0$.

Find the values of $k$ for which the following quadratic equation has equal roots:

$9x^2+kx+1=0$. Also, find the roots for those values of $k$ in each case.

Find the values of $k$ for which the following quadratic equation has equal roots:

$x^2-2kx+7k-12=0$. Also, find the roots for those values of $k$ in each case.

Find the value(s) of $p$ for which the quadratic equation $\left(2p+1\right)x^2-\left(7p+2\right)x+\left(7p-3\right)=0$ has equal roots. Also, find these roots.

Find the value(s) of $p$ for which the quadratic equation $2x^2+3x+p=0$ has real roots.

Find the least positive value of $k$ for which the equation $x^2+kx+4=0$ has real roots.

Find the values of $p$ for which the equation $3x^2-px+5=0$ has real roots.