Question

Write the zeros of the quadratic polynomial f(x) = 6x² − 3

Answer 1

To find the zeros of the quadratic polynomial we will equate f(x) to 0
$$\begin{gathered} \therefore f\left(x\right)=0 \\ \Rightarrow 6x^2-3=0 \\ \Rightarrow 3\left(2x^2-1\right)=0 \\ \Rightarrow 2x^2-1=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow 2x^2=1 \\ \Rightarrow x^2=\frac{1}{2} \\ \Rightarrow x=\pm \frac{1}{\sqrt{2}} \end{gathered}$$
Hence, the zeros of the quadratic polynomial f(x) = 6x² − 3 are $\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$.