Question

Use the words rational, irrational, or complex to describe the roots of the equation 20x² + 7x - 3 = 0?

1) Rational
2) Irrational
3) Complex

Answer 1

The roots of the equation 20x² + 7x - 3 = 0 are 1) rational numbers.

Step-by-step explanation:

The roots of the equation 20x² + 7x - 3 = 0 can be determined using the quadratic formula. For any quadratic equation of the form ax² + bx + c = 0, the discriminant (b² - 4ac) can help determine the nature of the roots.

In this case, a = 20, b = 7, and c = -3. Calculating the discriminant, we get: (7² - 4(20)(-3)) = 169. Since the discriminant is positive, the equation has two real roots.

Therefore, the roots of this equation are rational numbers. By solving the equation, we find that the roots are x = -0.35 and x = 0.15. Both of these solutions are rational numbers.