Sufficient/necessary condition or logical relationship involving a quadratic
The question frames a quadratic equation within a logical condition (sufficient, necessary) and asks to determine a parameter value ensuring the logical relationship holds.
For two conditions on real number $x$: $$\begin{aligned}
& p : x = a , \\
& q : 3 x ^ { 2 } - a x - 32 = 0
\end{aligned}$$ What is the value of positive $a$ such that $p$ is a sufficient condition for $q$? [3 points] (1) 1 (2) 2 (3) 3 (4) 4 (5) 5
3. Let- $1 < \mathrm { p } < 1$. Show that the equation $4 \mathrm { x } 2 - 3 \mathrm { x } - \mathrm { p } = 0$ has a unique root in the interval [1/2, 1] and identify it.