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Discriminant

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College Algebra

Definition

The discriminant is a value calculated from the coefficients of a quadratic equation $ax^2 + bx + c = 0$. It determines the nature and number of roots of the quadratic equation.

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5 Must Know Facts For Your Next Test

  1. The discriminant is given by the formula $D = b^2 - 4ac$.
  2. If $D > 0$, the quadratic equation has two distinct real roots.
  3. If $D = 0$, the quadratic equation has exactly one real root (a repeated root).
  4. If $D < 0$, the quadratic equation has two complex conjugate roots.
  5. The discriminant provides insight into whether the parabola corresponding to the quadratic equation intersects, touches, or does not intersect the x-axis.

Review Questions

  • What is the formula for calculating the discriminant of a quadratic equation?
  • What does it mean for a quadratic equation if its discriminant is zero?
  • How many real roots does a quadratic equation have if its discriminant is negative?
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