Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $9x^2 + 6x + 4 = 0$.

Is the following situation possible? If so,determine their present ages. The sum of the ages of two friends is $20$ years. Four years ago,the product of their ages in years was $48$.

If $b=0$ and $c < 0$,is it true that the roots of $x^{2}+bx+c=0$ are numerically equal and opposite in sign? Justify.

The value of the discriminant of a quadratic equation $kx^{2} - 4x - 4 = 0$ is $64$,then $k = \dots$

Which of the following groups correctly matches the data of Part $I$ with the data of Part $II$?

Part $I$	Part $II$
$1.$ The discriminant of $x^{2}+5x+6=0$	$a. 1$
$2.$ The discriminant of $x^{2}+5x+4=0$	$b. 9$
$3.$ The discriminant of $x^{2}+4x+3=0$	$c. 4$
$4.$ The discriminant of $x^{2}+6x+5=0$	$d. 16$

Find the discriminant of the following quadratic equation: $5x^{2} - 4\sqrt{2}x - 1 = 0$.