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Sagot :
[tex]\begin{gathered} x=\sqrt[]{2}\cdot i \\ x=-\sqrt[]{2}\cdot i \end{gathered}[/tex]
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
[tex]\begin{gathered} f(x)=3x^2+6 \\ f(x)=0 \\ \text{Hence} \\ 3x^2+6=0\text{ } \end{gathered}[/tex]Step 2
solve for x
[tex]\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} \\ \frac{3x^2}{3}=\frac{-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}[/tex]so, the answer is
[tex]\begin{gathered} x=\sqrt[]{2}\cdot i \\ x=-\sqrt[]{2}\cdot i \end{gathered}[/tex]I hope this helps you
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