Question

Use the discriminant to determine the number and type of solutions of the following quadratic equation. x²+7x−1=0

select the correct answer below:
A. there are two distinct rational solutions.
B. there are two distinct irrational solutions.
C. there are two complex solutions.
D. there is a single rational solution.

Answer 1

The quadratic equation x²+7x−1=0 has two distinct irrational solutions. Option B

Step-by-step explanation:

To determine the number and type of solutions of the quadratic equation x²+7x−1=0, we need to use the discriminant. The discriminant is the expression inside the square root of the quadratic formula, which is b² - 4ac. In this case, a = 1, b = 7, and c = -1. Substituting these values into the discriminant, we get 7² - 4(1)(-1) = 49 + 4 = 53.

Since the discriminant is positive (53 > 0) and not a perfect square, the quadratic equation has two distinct irrational solutions. Therefore, the correct answer is B. There are two distinct irrational solutions. Option B