How to Solve Quadratic Equations — Step by Step Guide

Step-by-Step Method

1. 1

   Write the equation in standard form ax² + bx + c = 0. Identify the values of a, b, and c.

2. 2

   Check if the equation can be factored easily. Look for two numbers that multiply to give ac and add to give b.

3. 3

   If factoring is difficult, use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. Calculate the discriminant D = b² - 4ac first.

4. 4

   If D > 0, there are two distinct real roots. If D = 0, there is one repeated root. If D < 0, there are no real roots.

5. 5

   Substitute back into the original equation to verify your answers.

Worked Example

Common Mistakes to Avoid

• ✗

  Forgetting to write the equation in standard form before applying the formula.

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  Making sign errors when substituting negative values of b or c into the quadratic formula.

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  Forgetting that ± means you need to calculate two separate values.

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  Not simplifying the final answer or leaving the square root unsimplified.

Practice Quadratic Equations on SparkEd

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Frequently Asked Questions

How do I solve Quadratic Equations problems?

Write the equation in standard form ax² + bx + c = 0. Identify the values of a, b, and c. Check if the equation can be factored easily. Look for two numbers that multiply to give ac and add to give b.

What are common mistakes in Quadratic Equations?

Forgetting to write the equation in standard form before applying the formula. Making sign errors when substituting negative values of b or c into the quadratic formula.

Which class covers Quadratic Equations?

Quadratic Equations is typically taught in Class 9, 10. SparkEd has free practice for all these grades.

Where can I practise Quadratic Equations for free?

SparkEd offers free chapter-wise practice for Quadratic Equations aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.