Question

Find the value of the discriminant for the quadratic equation. Then describe the number and type of roots for the equation. Use the words rational, irrational, or complex to describe the roots. 20x2+7x−3=0

Answer 1

The discriminant of the quadratic equation 20x^2 + 7x - 3 = 0 is 289, indicating that the equation has two distinct real roots.

Step-by-step explanation:

The quadratic equation given is 20x^2 + 7x - 3 = 0. To find the discriminant, we can use the formula: Δ = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.

For this equation, a = 20, b = 7, and c = -3. Substituting these values into the formula, we have: Δ = (7)^2 - 4(20)(-3).

Simplifying this expression, we get: Δ = 49 + 240 = 289.

The discriminant, Δ, is equal to 289. Now, let's determine the number and type of roots based on the value of the discriminant:

• If Δ > 0, there are two distinct real roots.
• If Δ = 0, there is one real root (repeated).
• If Δ < 0, there are two complex roots (conjugates of each other).

Since Δ = 289, which is greater than 0, the quadratic equation has two distinct real roots.