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Advanced Math

Course covering algebra, calculus, and mathematical reasoning, develop analytical skills and prepare students for complex, higher-level mathematical challenges.

Advanced Math

Course covering algebra, calculus, and mathematical reasoning, develop analytical skills and prepare students for complex, higher-level mathematical challenges.

Understanding the Quadratic Formula

0:13

The Discriminant and the Nature of Roots

6 min read

Quadratic Formula and Discriminant Quiz

5 tasks

Understanding the Quadratic Formula

0:13
Apr 4, 2026
Free

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The Discriminant and the Nature of Roots
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Video Details

Understanding the Quadratic FormulaLink to understanding-the-quadratic-formula

A short video lesson on solving quadratic equations of the form

ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0

using the quadratic formula

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​

The discriminant Δ=b2−4ac\Delta = b^2 - 4acΔ=b2−4ac decides how many real solutions exist.

What you'll learn
  • Identify the coefficients aaa, bbb, ccc
  • Compute the discriminant Δ=b2−4ac\Delta = b^2 - 4acΔ=b2−4ac
  • Two real roots when Δ>0\Delta > 0Δ>0
  • One repeated root x=−b2ax = -\frac{b}{2a}x=−2ab​ when Δ=0\Delta = 0Δ=0
  • Complex roots when Δ<0\Delta < 0Δ<0

Worked exampleLink to understanding-the-quadratic-formula-worked-example

Solve 2x2+3x−2=02x^2 + 3x - 2 = 02x2+3x−2=0:

x=−3±254=−3±54x = \frac{-3 \pm \sqrt{25}}{4} = \frac{-3 \pm 5}{4}x=4−3±25​​=4−3±5​x=12orx=−2x = \frac{1}{2} \quad \text{or} \quad x = -2x=21​orx=−2

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