In a polynomial, what term refers to the quantity computed from the coefficients that gives information about the roots?

• A. A function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial.
• B. The possible value of y.
• C. The range.
• D. A parallelogram with 4 right angles.

Answer: (A)

The discriminant is the quantity you’re looking for. It is a function of the polynomial’s coefficients that tells you about the roots’ nature. For a quadratic with coefficients a, b, and c, the discriminant is b^2 − 4ac. Its value flags what the roots look like: if it’s positive, you have two distinct real roots; if it’s zero, the roots are real and equal (a repeating root); if it’s negative, the roots are complex conjugates. More generally, the discriminant is a polynomial in the coefficients that vanishes exactly when the polynomial has a multiple root, so its value gives information about the roots’ existence and multiplicity. The other options don’t relate to roots in this way—the possible value of y is just an outcome, the range concerns outputs, and a parallelogram with four right angles is a rectangle, not about polynomial roots.