4.8 Quadratic Formula and Discriminant

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4.8 Quadratic Formula and Discriminant

Quadratic Formula Formula: x = -b ± √(b2 – 4ac) 2a This formula can be used to solve any quadratic equation. Equations must be written in standard form. Identify: a = b = c = When solving the formula use order of operations.

Examples: Solve the equations below: (Ex1) x2 + 3x = 2

Equation with One Solution Solve the equation below: (Ex2) 25x2 – 18x = 12x – 9

Equation with Imaginary Solution Solve the equation below: (Ex3) -x2 + 4x = 5

Discriminant Formula: b2 – 4ac Discriminant informs you how many and what type of solutions there are to a quadratic equation. Types of Solutions: 1) # > 0 2 real solutions 2) # = 0 1 real solution 3) # < 0 2 imaginary solutions

Examples: How many solutions are there to the equation below? x2 – 8x + 17 = 0

Determine if the equation has a real solution or an imaginary solution. 7x2 – 2x = 5