Solve an equation with two real solutions

1
EXAMPLE 1
Solve an equation with two real solutions
Solve x2 3x 2.
x2 3x 2
Write original equation.
x2 3x 2 0
Write in standard form.
Quadratic formula
a 1, b 3, c 2
Simplify.
2
EXAMPLE 1
Solve an equation with two real solutions
CHECK
Graph y x2 3x 2 and note that the
x-intercepts are about 0.56 and about 3.56.
?
3
EXAMPLE 2
Solve an equation with one real solutions
Solve 25x2 18x 12x 9.
25x2 18x 12x 9.
Write original equation.
25x2 30x 9 0.
Write in standard form.
a 25, b 30, c 9
Simplify.
Simplify.
4
EXAMPLE 2
Solve an equation with one real solutions
CHECK
Graph y 5x2 30x 9 and note that the only
x-intercept is 0.6 .
3
?
5
5
EXAMPLE 3
Solve an equation with imaginary solutions
Solve x2 4x 5.
x2 4x 5
Write original equation.
x2 4x 5 0.
Write in standard form.
a 1, b 4, c 5
Simplify.
Rewrite using the imaginary unit i.
x 2 i
Simplify.
6
EXAMPLE 3
Solve an equation with imaginary solutions
CHECK
Graph y 2x2 4x 5. There are no
x-intercepts. So, the original equation has no
real solutions. The algebraic check for the
imaginary solution 2 i is shown.
7
for Examples 1, 2, and 3
GUIDED PRACTICE
Use the quadratic formula to solve the equation.
x2 6x 4

3 5
ANSWER
4x2 10x 2x 9

1
ANSWER
7x 5x2 4 2x 3

ANSWER