Question

Find the roots of the equation 3x^2 + 45 = 0.

Answer 1

$+i\sqrt{15}\text{ ,-i}\sqrt{15}$

Explanation

A root is a value for which a given function equals zero, so let's solve the equation

Step 1

$3x^2+45=0$

a) apply the subtraction property of equality and subtract 45 in both sides

$\begin{gathered} 3x^2+45=0 \\ 3x^2+45-45=0-45 \\ 3x^2=-45 \end{gathered}$

b)now, use the division property of equality to isolate square x,

$\begin{gathered} 3x^2=-45 \\ divide\text{ both sides by 3} \\ \frac{3x^2}{3}=\frac{-45}{3} \\ x^2=-15 \end{gathered}$

c) finally , take the square root in both sides

$\begin{gathered} x^{2}=-15 \\ \sqrt{x^2}=\sqrt{-15} \\ x=\pm\sqrt{15}i \\ x=\pm i\sqrt{15} \end{gathered}$

so, the answer is

$+i\sqrt{15}\text{ ,-i}\sqrt{15}$

I hope this helps you