Question

Use the discriminant to determine the number and types of roots of the quadratic equation., 4x² - 71x +1 = -5

The discriminant is ____than 0, so there are ___ ___roots.

Answer 1

The discriminant is positive, so there are two distinct real roots.

Step-by-step explanation:

To determine the number and types of roots of a quadratic equation, we can use the discriminant.

The discriminant is calculated using the formula b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

In the equation 4x^2 - 71x +1 = -5, the coefficients are a = 4, b = -71, and c = 1-(-5) = 6.

Plugging these values into the discriminant formula, we have:

Discriminant = (-71)^2 - 4(4)(6) = 5041 - 96 = 4945

Since the discriminant is positive, there are two distinct real roots.