Question

What are the exact solutions of x^2 – 5x - 1 = 0 using X = -b ± √(b^2 - 4ac) / 2a?

Answer 1

The quadratic equation x^2 - 5x - 1 = 0 has solutions x = (5 + √29) / 2 and x = (5 - √29) / 2. Approximate values are x ≈ 5.19 and x ≈ -0.19.

Step-by-step explanation:

The exact solutions for the quadratic equation x^2 – 5x - 1 = 0 can be found using the quadratic formula x = -b ± √(b^2 - 4ac) / (2a). Here, the coefficients are a = 1, b = -5, and c = -1.

First, we compute the discriminant: √((-5)^2 - 4(1)(-1)) which simplifies to √(25 + 4) or √29. Then we apply the quadratic formula:

x = (-(-5) ± √29) / (2 * 1)

• x = (5 ± √29) / 2

The two exact solutions are:

• x = (5 + √29) / 2
• x = (5 - √29) / 2

These can be approximated as x ≈ 5.19 and x ≈ -0.19 respectively.