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DOC

Algebra Basics.pdf

Chapter 3: Quadratic Equations

📐 Quadratic Equations

A quadratic equation is a polynomial equation of degree 2.

Standard Form

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

where a, b, and c are constants, and a ≠ 0.

🎯 The Quadratic Formula

The solutions to any quadratic equation can be found using:

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

📊 The Discriminant

The expression under the square root is called the discriminant:

Δ=b2−4ac\Delta = b^2 - 4ac
  • •If Δ>0\Delta > 0: Two real solutions
  • •If Δ=0\Delta = 0: One real solution
  • •If Δ<0\Delta < 0: No real solutions

✏️ Example

Solve: x2−5x+6=0x^2 - 5x + 6 = 0

Here, a = 1, b = -5, c = 6

x=5±25−242=5±12x = \frac{5 \pm \sqrt{25 - 24}}{2} = \frac{5 \pm 1}{2}

Solutions: x=3x = 3 or x=2x = 2

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What is the Quadratic Formula?

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

1 of 4 • Click card to flip

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Question 1 of 4
0/4

What is the solution to x2−4=0x^2 - 4 = 0?

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Algebra_Textbook.pdf

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