Final answer:
The part of the quadratic formula (b² - 4ac) is known as the discriminant, which determines the nature of a quadratic equation's roots.
Step-by-step explanation:
The part of the quadratic formula (b² - 4ac) is known as the discriminant.
The discriminant can tell us the nature of the roots of a quadratic equation of the form ax² + bx + c = 0.
If b² - 4ac > 0, there are two distinct real roots. If b² - 4ac = 0, there is one real root (a repeated root).
If b² - 4ac < 0, there are two complex roots.
For the quadratic equation at² + bt + c = 0, with constants a = 4.90, b = 14.3, and c = -20.0, we would use this part of the formula to determine the nature of its solutions.