____ is the expression, b^2-4ac which tells the nature of the roots of a quadratic equation of the form ax^2+bx+c=0

Answer 1

The expression \( b^2 - 4ac \) is called the discriminant of a quadratic equation of the form \( ax^2 + bx + c = 0 \). The value of the discriminant helps determine the nature of the roots of the equation:

• If \( b^2 - 4ac > 0 \): The equation has two distinct real roots.
• If \( b^2 - 4ac = 0 \): The equation has exactly one real root (or a repeated real root).
• If \( b^2 - 4ac < 0 \): The equation has two complex conjugate roots (no real roots).