Question

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

Answer 1

`+i√(15)\text{ ,-i}√(15)`

Step-by-step 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} \\ (3x^2)/(3)=(-45)/(3) \\ x^2=-15 \end{gathered}`

c) finally , take the square root in both sides

`\begin{gathered} x^(2)=-15 \\ √(x^2)=√(-15) \\ x=\pm√(15)i \\ x=\pm i√(15) \end{gathered}`

so, the answer is

`+i√(15)\text{ ,-i}√(15)`

I hope this helps you