Download Extra Support for Chapter 10

Solving Quadratic Equations
1. Solve. x2 = 100
x  100
2
x   100
x  10
x  {10, 10}
Take the square root of
both sides.
2
Do not forget the ±.
The solution set has
two answers.
2. Solve. x2 = 20
x  20
2
Take the square root of
both sides.
x   20 Do not forget the ±.
Simplify the square root.
x  2 5
The solution set has
x  {2 5 , 2 5} two answers.
2
3. Solve. y2 = -64
y  64
Anticipate imaginary
solutions.
2
y    64
y  8i
y  {8i, 8i}
2
Take the square root of
both sides.
Do not forget the ±.
Simplify the square root.
The solution set has
two answers.
4. Solve. (x + 1)2 = 4
( x  1)  4
x  1 2
2
x


3
( x  1)   4
x


1
2
x  1  2
x

1
x  1 2
Work it twice ±.
x  {3, 1}
2
5. Solve this quadratic equation by
factoring.
2
x  10 x  24  0
( x  6)( x  4)  0 Zero factor
x6  0 x4  0
x  6 x  4
x  {6,  4}
6. Solve this quadratic equation by
completing the square.
x2 + 10x + 24 = 0
25
25
+ 10x + _______ = - 24 + ________
5 2 = ______
1
( x + _____)
5
1
x + _____ = ± _______
x2
-5 ± 1
x = ________
x

{

6
,

4
}
-6
-4
x = {______,
______}
7. Solve. x2 = -81
x  81
Anticipate imaginary
solutions.
2
x    81
x  9i
x  {9i, 9i}
Take the square root of
both sides.
2
Do not forget the ±.
Simplify the square root.
The solution set has
two answers.
8. Which of the following equations has
a solution set of x = {9, -5}?
x2
x=9, x=-5
+ 4x + 45 B.
x2 + 4x – 45 C.
(x – 9)(x + 5) =
x2 – 4x – 45
0
2
D. x – 4x + 45
A.
x2 – 4x – 45 = 0
9. What is the sum of the solutions to
2
the quadratic y – 15y +56=0?
A.
B.
C.
D.
3
-3
15
-15
y2 – 15y + 56 = 0
(y – 7)(y – 8) = 0
y = { 7, 8}
Hence…
7 + 8 = 15
10. The quadratic equation
2
x + 5x + 25/4 = 0 has…
A. one real rational
solutions.
B. two real irrational
solutions.
C. two real rational
solution.
D. two complex
solutions.
E. one complex
solution.
D = b2 – 4ac
D = (5)2 – 4(1)(25/4)
D = 25 – 25
D=0