Question 26

Explanation

Combine like terms so the function becomes

with $a = m - 2$, $b = 2m$ and $c = m - 3$.

The condition for the function to always be below the $x$ axis is $D < 0$ and $a < 0$.

Finding the discriminant value

Finding the coefficient value

The intersection of both solutions is $m < 1\frac{1}{5}$.

Therefore, the value of $m$ below the $x$ axis that is possible is $m < 1\frac{1}{5}$.