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