Final answer:
The solutions of the quadratic equation x² + 10 = 0 are imaginary.
Step-by-step explanation:
The solutions of the quadratic equation x² + 10 = 0 can be found by rearranging the equation to get it in the standard quadratic form, which is ax² + bx + c = 0. In this case, we have x² + 0x + 10 = 0. Since there is no x term, we can directly apply the quadratic formula to find the solutions.
To find the solutions of a quadratic equation of the form ax² + bx + c = 0, we use the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / (2a)
Applying the Quadratic Formula:
In our given equation, a = 1, b = 0, and c = 10. Plugging these values into the quadratic formula, we get:
x = (-0 ± sqrt(0² - 4(1)(10))) / (2(1))
x = (± sqrt(-40)) / 2
Since we have a negative value inside the square root, the solutions of the quadratic equation x² + 10 = 0 are imaginary. Therefore, there are no real solutions to this quadratic equation.