Question

Which of the following best describes the roots of the equation x^2 - 6x + 10 = 0?

A) 2 imaginary roots
B) 2 real roots
C) 1 real 1 imaginary root
D) 1 real root.

Answer 1

The roots of the equation x^2 - 6x + 10 = 0 are 2 imaginary roots.

Step-by-step explanation:

The equation x^2 - 6x + 10 = 0 represents a quadratic equation. The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / (2a).

In this case, a = 1, b = -6, and c = 10. Plugging these values into the quadratic formula, we get x = (6 ± sqrt((-6)^2 - 4(1)(10)) / (2(1)). The roots of the equation x^2 - 6x + 10 = 0 can be determined using the quadratic formula, which is applied to equations of the form ax^2 + bx + c = 0. The discriminant, given by b^2 - 4ac, helps us to understand the nature of the roots.

For the given equation, the discriminant can be calculated as (-6)^2 - 4(1)(10) = 36 - 40 = -4. Since the discriminant is negative, this means the equation has two imaginary roots. No real roots exist when the discriminant is less than zero. Thus, the correct answer is (A) 2 imaginary roots.

Calculating this expression, we find that the discriminant, which is the part inside the square root, is negative. Therefore, the roots of the equation are 2 imaginary roots. So the answer is:

Option A) 2 imaginary roots