Find solutions to your questions with the help of IDNLearn.com's expert community. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

Select the correct answer.

What are the solutions of this quadratic equation?

[tex]\[ x^2 + 10 = 0 \][/tex]

A. [tex]\( x = \pm \sqrt{10} \)[/tex]

B. [tex]\( x = \pm 5 \)[/tex]

C. [tex]\( x = \pm \sqrt{10} i \)[/tex]

D. [tex]\( x = \pm 5i \)[/tex]


Sagot :

To solve the quadratic equation [tex]\( x^2 + 10 = 0 \)[/tex], let's follow the steps:

1. Isolate the quadratic term: We need to isolate [tex]\( x^2 \)[/tex] on one side of the equation. We can do this by subtracting 10 from both sides:
[tex]\[ x^2 + 10 - 10 = 0 - 10 \][/tex]
Simplifying this, we get:
[tex]\[ x^2 = -10 \][/tex]

2. Take the square root of both sides: To solve for [tex]\( x \)[/tex], we take the square root of both sides of the equation. Remember, when taking the square root of a negative number, we use the imaginary unit [tex]\( i \)[/tex], where [tex]\( i = \sqrt{-1} \)[/tex]:
[tex]\[ x = \pm \sqrt{-10} \][/tex]

3. Simplify the square root: The square root of [tex]\(-10\)[/tex] can be written using the imaginary unit [tex]\( i \)[/tex]:
[tex]\[ x = \pm \sqrt{10} \cdot \sqrt{-1} = \pm \sqrt{10} i \][/tex]

Therefore, the solutions to the equation [tex]\( x^2 + 10 = 0 \)[/tex] are:
[tex]\[ x = \pm \sqrt{10} i \][/tex]

By examining the given answer choices, the correct one is:

C. [tex]\( x = \pm \sqrt{10} i \)[/tex]