solving quadratic equations. 1. solve. x 2 = 100 take the square root of both sides. do not forget...
TRANSCRIPT
Solving Quadratic Equations
1. Solve. x2 = 100
1002 x
1002 x
Take the square root of both sides.
Do not forget the ±.
10x}10,10{x
The solution set has two answers.
2. Solve. x2 = 20
202 x
202 x
Take the square root of both sides.
Do not forget the ±.
52x}52,52{x
The solution set has two answers.
Simplify the square root.
3. Solve. y2 = -64
642 y
642 y
Take the square root of both sides.
Do not forget the ±.
iy 8}8,8{ iiy The solution set has
two answers.
Simplify the square root.
Anticipate imaginary solutions.
4. Solve. (x + 1)2 = 4
4)1( 2 x
4)1( 2 x21 x
}1,3{x21x
21x3x21x
1xWork it twice ±.
5. Solve this quadratic equation by factoring.
024102 xx0)4)(6( xx Zero factor
06 x6x
04 x4x}4,6{ x
6. Solve this quadratic equation by completing the square.
x2 + 10x + 24 = 0
x2 + 10x + _______ = - 24 + ________
( x + _____)2 = ______
x + _____ = ± _______
x = ________
x = {______, ______}
525 25
1
15
-5 ± 1
-6 -4 }4,6{ x
7. Solve. x2 = -81
812 x
812 x
Take the square root of both sides.
Do not forget the ±.
ix 9}9,9{ iix The solution set has
two answers.
Simplify the square root.
Anticipate imaginary solutions.
8. Which of the following equations has a solution set of x = {9, -5}?
A. x2 + 4x + 45 B.
x2 + 4x – 45 C. x2 – 4x – 45
D. x2 – 4x + 45
x=9, x=-5
(x – 9)(x + 5) = 0
x2 – 4x – 45 = 0
9. What is the sum of the solutions to
the quadratic y2 – 15y +56=0?
A. 3
B. -3
C. 15
D. -15
y2 – 15y + 56 = 0
(y – 7)(y – 8) = 0
y = { 7, 8}
Hence…
7 + 8 = 15
10. The quadratic equation x2 + 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