Question

F(x)=3x^2+6. find the zeros. there is 2 of them

Answer 1

`\begin{gathered} x=\sqrt[]{2}\cdot i \\ x=-\sqrt[]{2}\cdot i \end{gathered}`

Step-by-step explanation

The zero of a function is any replacement for the variable that will produce an answer of zero,so let f(x)=o to find the zeros

Step 1

Let f(x)= 0 and solve for x

`\begin{gathered} f(x)=3x^2+6 \\ f(x)=0 \\ \text{Hence} \\ 3x^2+6=0\text{ } \end{gathered}`

Step 2

solve for x

`\begin{gathered} 3x^2+6=0\text{ } \\ subtract\text{ 6 in both sides} \\ 3x^2+6-6=0-6\text{ } \\ 3x^2=-6 \\ \text{divide boths sides by 3} \\ (3x^2)/(3)=(-6)/(3) \\ x^2=-2 \\ \text{remember i}^2=-1,\text{ }i=\sqrt[]{-1} \\ \text{hence} \\ x=\pm\sqrt[]{-2} \\ x=\pm\sqrt[]{2\cdot-1\text{ }} \\ x=\pm\sqrt[]{2}\cdot\sqrt[]{-1} \\ x=\pm\sqrt[]{2}\cdot i \\ \end{gathered}`

so, the answer is

`\begin{gathered} x=\sqrt[]{2}\cdot i \\ x=-\sqrt[]{2}\cdot i \end{gathered}`

I hope this helps you