SAT-Style: Discriminant and Number of Solutions

SAT Math · Axiom Academy

Discriminant & Number of Solutions Determine Solutions Without Solving For a quadratic , the discriminant is: Δ > 0 → 2 real solutions (parabola crosses x-axis twice) Δ = 0 → 1 real solution (parabola touches x-axis once) Δ < 0 → 0 real solutions (parabola doesn't touch x-axis) We want: exactly 1 solution, so Δ = 0 When k = 8, the quadratic becomes , which has discriminant (8)² - 4(1)(16) = 64 - 64 = 0. Perfect! It touches the x-axis at exactly one point.

This is the written version of the interactive lesson above. See the full SAT Math course.