Question

Which two values of x are roots of the polynomial below? 4x^2 - 6x + 1

Answer 1

The two roots of the polynomial 4x^2 - 6x + 1 are found using the quadratic formula, providing the approximate values of 1.306 and 0.191.

Step-by-step explanation:

The roots of the polynomial 4x^2 - 6x + 1 can be found using the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a) for any quadratic equation of the form ax^2 + bx + c = 0. In this case, a = 4, b = -6, and c = 1.

Plugging these values into the quadratic formula gives us:

x = (6 ± √((-6)^2 - 4 * 4 * 1)) / (2 * 4)

x = (6 ± √(36 - 16)) / 8

x = (6 ± √20) / 8

Since √20 is approximately 4.472, this gives us two roots:

• x = (6 + 4.472) / 8
• x = (6 - 4.472) / 8

Which simplifies to:

• x ≈ 1.306
• x ≈ 0.191

Therefore, the two roots of the polynomial are approximately 1.306 and 0.191.