Question

Find the roots of the equation x²-2x+9=0 Additionally, what does the discriminant tell you about the solution?

A) The roots are real and equal. The discriminant is greater than zero.

B) The roots are imaginary. The discriminant is less than zero.

C) The roots are real and distinct. The discriminant is greater than zero.

D) The equation has no real roots. The discriminant is equal to zero

Answer 1

The roots of the quadratic equation x²-2x+9=0 are imaginary, as the discriminant is -32, which is less than zero. Using the quadratic formula, the equation would yield two complex roots but not real roots.

Step-by-step explanation:

To find the roots of the quadratic equation x²-2x+9=0, we use the quadratic formula:

`x = [-b\± √(b^2-4ac) ] / (2a)`, where a=1, b=-2, and c=9.

The discriminant (Δ) is defined as b²-4ac.

In our case, Δ = (-2)² - 4(1)(9) = 4 - 36 = -32.

Since the discriminant is less than zero (Δ < 0), the equation does not have real roots; instead, it has two complex roots. Therefore, the correct answer here is B) The roots are imaginary. The discriminant is less than zero.