Given: $X = \sqrt{e - 4}$ Write down the value of $e$, for which $X$ is: 2.1.1 Zero 2.1.2 Non-real 2.2 Determine the value(s) of $m$ for which the equation $mx^2 - 12x + 9 = 0$ has equal roots. - NSC Technical Mathematics - Question 2 - 2022 - Paper 1

For $X$ to be non-real, the expression inside the square root must be negative:

$e - 4 < 0$
This leads to: $e < 4$

To determine the values of $m$ for which the equation has equal roots, we need to use the discriminant condition:

$\Delta = b^2 - 4ac = 0$
Here, we identify $a = m$, $b = -12$, and $c = 9$. Substituting these values into the discriminant formula gives us:

$\Delta = (-12)^2 - 4(m)(9) = 0$
Calculating $(-12)^2$ results in $144$, so the equation simplifies to:

$144 - 36m = 0$
Rearranging this gives:

$36m = 144$
Finally, dividing by 36 yields:

$m = 4$