Question

Is $x=3$ a solution of the equation $2x^2-5x-3=0$?

Answer 1

Step 1: State the factor theorem.

Given equation: $2x^2-5x-3=0$.

Let us assume that, $p\left(x\right)=0$, here, $p\left(x\right)=2x^2-5x-3$.

If, $x=a$ is a solution to the equation $p\left(x\right)=0$, then $p\left(a\right)=0$.

Step 2: Apply the factor theorem.

Put $x=3$ in the given equation.

$$\begin{gathered} p\left(3\right)=2{\left(3\right)}^2-5\left(3\right)-3 \\ p\left(3\right)=18-15-3 \\ p\left(3\right)=0 \end{gathered}$$

Hence, $p\left(3\right)=0$.

Therefore, $x=3$ is a solution to the given equation $2x^2-5x-3=0$.