Page 759 - Algebra 1

Example
3
Finding Approximate Solutions
Use the quadratic formula to solve for x. Then use a graphing calculator to find approximate solutions and verify them.
5x2 -3x-1=0
SOLUTION
5x2 -3x-1=0
__ x = 2a
2
- b ± √ b - 4 a c
Use the quadratic formula. Substitute the values for a, b, and c.
___ 2(5)
= -(-3) ± √(-3)2 - 4(5)(-1)
x = 3 ± √9 + 2 0 = 3 ± √2 9 ___
10 10
To find the approximate solutions, use a calculator with a square root key. Round the solutions to the nearest ten thousandth.
Check
On a graphing calculator, graph the related function y = 5x2 - 3x - 1 to check that the approximate solutions are the zeros of the graph.
Recognizing a Quadratic Equation With No Real Solutions
__
The solutions are 3 + √2 9 ≈ 0.8385 and 3 - √2 9 ≈ -0.2385.
10 10
Graphing Calculator Tip
For help with graphing quadratic equations, see the graphing calculator keystrokes in Lab 8 on
p. 583.
Example
4
744 Saxon Algebra 1
Use the quadratic formula to solve 2x2 + 3x + 4 = 0 for x. SOLUTION
__ 2a
2
- b ± √ b - 4 a c
x=
= -(3) ± √(3)2 - 4(2)(4)
___ 2(2)

Substitute the values for a, b, and c. x = -3 ± √9 - 3 2 = -3 ± √- 2 3
____ 44
The square root of a negative number cannot be taken, so there are no real solutions.