Quadratic Formula in 5 Minutes — Free Quick Revision

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TL;DR: Learn Quadratic Formula in about 5 minutes — a free bite-sized module with a clear explanation, a worked example and a quick quiz for Indian students.

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The quadratic formula x = (-b ± √(b² - 4ac)) / 2a solves any quadratic equation instantly. No factoring needed.

Maths · Class 10 · about 6 minutes

The Idea

A quadratic equation has the form ax² + bx + c = 0, where a ≠ 0. Sometimes these are hard to factor, so mathematicians derived the quadratic formula.

The formula is: x = (-b ± √(b² - 4ac)) / 2a

The part under the square root, b² - 4ac, is called the discriminant. It tells you how many real solutions exist: - If discriminant > 0: two different real roots - If discriminant = 0: one repeated root - If discriminant < 0: no real roots (only complex)

Just plug in your a, b, c values and compute. The ± means you'll get two answers (one with +, one with −).

Worked Example: Solve 2x² - 5x + 3 = 0

Problem. Find x using the quadratic formula where a = 2, b = −5, c = 3.

Solution.

x = (-(-5) ± √((-5)² - 4(2)(3))) / 2(2) x = (5 ± √(25 - 24)) / 4 x = (5 ± √1) / 4 x = (5 ± 1) / 4

So x = (5 + 1) / 4 = 6/4 = 3/2, or x = (5 - 1) / 4 = 4/4 = 1

Answer: x = 3/2 or x = 1

Quick Quiz

Answer each one before reading the explanation beneath it.

1. Using the quadratic formula for x² - 4 = 0, what is the discriminant b² - 4ac?

• 0
• 16 — correct
• -16
• 4

16

2. What does a discriminant of 0 mean?

• Two different real roots
• One repeated root (double root) — correct
• No real roots
• Three roots

One repeated root (double root)

3. Solve 3x² + 0x - 12 = 0 using the quadratic formula. What are the roots?

• x = 2 or x = -2 — correct
• x = 4 or x = -4
• x = 1 or x = -1
• No real roots

x = 2 or x = -2

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