Final: No Real Roots

Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 50 of 51.

Solve the equation on the board. Its discriminant is negative, so the parabola never touches the x-axis and there are no real solutions. Find the two complex ones and write them with i.

Challenge

Solve 2x^2 - 4x + 5 = 0. It has no real solutions: find both complex ones.

Try it yourself

2x^2 - 4x + 5 = 0

Solve for x

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Quadratics & Complex Numbers

1The Vertex

The Axis of Symmetry The Vertex Point Maximum or Minimum Drawing from Standard Form Recap: The Vertex

4Imaginary Numbers

Meet i Roots of Negatives Not a Perfect Square Powers of i Recap: Imaginary Numbers

7The Discriminant

Computing It Three Kinds of Answers Reading the Sign Recap: The Discriminant

10Final Challenges

Final: Square It Away Final: The Peak Final: Divide ItFinal: No Real RootsFinal: Where They Meet

2Completing the Square

Perfect Square Trinomials The Missing Number Completing the Square Irrational Answers When a Is Not 1 Recap: Completing the Square

5Complex Arithmetic

Adding and Subtracting Multiplying The Conjugate Dividing A Pure Imaginary Bottom Recap: Complex Arithmetic

8Lines Meet Parabolas

Two Crossings Just Touching No Meeting A Circle and a Line Recap: Lines and Parabolas

3Vertex Form by Algebra

From Standard to Vertex Odd Middle Terms A Leading Number Opening Down Recap: Vertex Form

6Complex Solutions

Squares Equal to Negatives A Shifted Square The Formula Goes Complex Fractions in the Answer Recap: Complex Solutions

9Quadratic Models

The Highest Point Back to the Ground The Biggest Area Price and Revenue Recap: Models