Question

What are the solutions of this quadratic equation? x² + 10 = 0.

A) x = ± sqrt(10)
B) x = ± 5
C) x = ± sqrt(10)i
D) x = ± 5i

Answer 1

To find the solutions of the quadratic equation x² + 10 = 0, we use the quadratic formula. The solutions are complex numbers: x = ± √(10)i.

Step-by-step explanation:

To find the solutions of the quadratic equation x² + 10 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions can be found using the formula x = (-b ± √(b² - 4ac))/(2a).

In this case, a = 1, b = 0, and c = 10. Substituting these values into the formula, we get x = (-0 ± √(0² - 4(1)(10)))/(2(1)). Simplifying further, x = ± √(-40)/2.

Since the square root of a negative number is not a real number, the solutions of this quadratic equation are complex numbers. Therefore, the correct answer is C) x = ± √(10)i.