Question

1. what does it mean when the discriminant of a quadratic equation is zero?

a. the equation has no solution
b. the equation has one real solution
c. the equation has two distinct real solutions
d. the equation has two complex solutions

Explanation:

For a quadratic equation \( ax^{2}+bx + c = 0\) (\(a
eq0\)), the discriminant is given by \( D=b^{2}-4ac\).

• If \( D>0\), the equation has two distinct real solutions.
• If \( D = 0\), the equation has one real solution (a repeated root, or a root with multiplicity 2).
• If \( D<0\), the equation has two complex conjugate solutions.

So when the discriminant is zero, the quadratic equation has one real solution.

Answer:

b. The equation has one real solution