What are the solutions to this quadratic equation?x^2+10=0
1 answer:
Answer:
<em>Correct choice: C.</em> ![x=\pm\sqrt{10}\mathbf{i}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B10%7D%5Cmathbf%7Bi%7D)
Step-by-step explanation:
The quadratic equation to solve is:
![x^2+10=0](https://tex.z-dn.net/?f=x%5E2%2B10%3D0)
Since this equation is incomplete, we can solve it without using the quadratic solver formula.
Subtracting 10:
![x^2=-10](https://tex.z-dn.net/?f=x%5E2%3D-10)
Taking square root:
![x=\pm\sqrt{-10}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B-10%7D)
Recall the square root of a negative number leads to imaginary solutions where the Unit Imaginary Number (i) is used, where:
![\mathbf{i}=\sqrt{-1}](https://tex.z-dn.net/?f=%5Cmathbf%7Bi%7D%3D%5Csqrt%7B-1%7D)
The solutions to the equation are:
![x=\pm\sqrt{10}\mathbf{i}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B10%7D%5Cmathbf%7Bi%7D)
Correct choice: C. ![x=\pm\sqrt{10}\mathbf{i}](https://tex.z-dn.net/?f=x%3D%5Cpm%5Csqrt%7B10%7D%5Cmathbf%7Bi%7D)
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