Question

Look at the quadratic equation below:

x^2 - 6x + 10 = 0
Find the discriminant of the equation and determine the number of and type of solutions of the equation.
a) The discriminant is 4, and the equation has two real solutions.
b) The discriminant is 4, and the equation has one distinct real solution.
c) The discriminant is 4, and the equation has two imaginary solutions.
d) The discriminant is -4, and the equation has one distinct imaginary solution.

Answer 1

The discriminant of the quadratic equation x^2 - 6x + 10 = 0 is -4, indicating that the equation has two imaginary solutions.

Step-by-step explanation:

To find the discriminant of the quadratic equation x^2 - 6x + 10 = 0 and determine the number and type of solutions it has, we can use the discriminant formula D = b^2 - 4ac, where a, b, and c are coefficients of the quadratic equation ax^2 + bx + c = 0. In this equation, a = 1, b = -6, and c = 10. Plugging these values into the discriminant formula, we get:

D = (-6)^2 - 4(1)(10)
D = 36 - 40
D = -4

Since the discriminant is negative (D = -4), it indicates that this quadratic equation has two imaginary solutions. This corresponds to option d.