Chapter 5 - Quadratic Equation

Question 1

Quadratic formula

Answer 1

ax² + bx + c = 0

1) Set the equation equal to 0.
2) a is usually 1. If a is not 1, divide the equation through a
3) Find two integers whose product equals c and whose sum equals b.

Question 2

Disguised quadratic

G/R: If you have a quadratic expression equal to 0, AND you can factor an x out of the expression, then x=0 is a solution of the expression

** Be careful not to just divide both sides by x. This will improperly eliminate the solution x=0.

Answer 2

1) 3w²= 6w

3w² - 6w= 0

w ( 3w-6) = 0

w=0; w=2

2) 36/b= b-5

36= b²- 5b

3) x³+ 2x²-3x

x( x²+ 2x-3) =0

Question 3

Taking a Square root of a quadratic

Answer 3

If the other side of the equation is a perfect square quadratic, prob can be solved quickly by taking square root of both sides of the equation

If (z+3)² =25, What is z?

√(z+3)²= √25

(z+3) = ± 5

z= 2, -8

Remember: Since you are taking th square root, use both positive and negative square root.

Question 4

Using FOIL with Square Roots

Answer 4

What is value of (√8-√3)(√8+ √3)?

F: √8* √8= √64= 8

O: √8*√3 = √24

I: (-√3) * √8 = -√24

L: (-√3) * √3 = -√9 = -3

8 + √24 - √24 - 3

8-3 = 5

Question 5

One Solution Quadratic

Answer 5

One solution quadratic are also called **perfect square **quadratics.

x²+ 8x + 16=0

(x+4) ( x+4)= 0

Only one solution for x =-4

** Always factor quadratic equations to determine their solutions

Question 6

Zero in the den: expression becomes undefined

Answer 6

Zero in the den: expression becomes undefined

Question 7

Memorize: Three Special Products

Answer 7

S.P #1: x²- y²= (x+y) (x-y)

S.P #2: ** x^{2<strong></strong>}+** 2xy + y²= (x+y)(x+y)= (x+y)²

S.P #3: x²- 2xy + y²= (x-y)(x-y) = (x-y)²

Disguise: a² -1: (a+1) (a-1)

**Disguise: **(a+b)²= a²+ 2ab + b²

Question 8

Given that (p-3)² - 5=0, what is p?

Since there is (p-3)² in this question, you will be tempted to solve this via the quadratic method but there are no factors for it using quadratc. Solve using alternative approach.

Answer 8

Another Method:

(p-3)² - 5 = 0

(p-3)² = 5

√(p-3)² = √5 ⇒ Cancel ²(square root) with √ sign

(p-3) = ± √5

p = 3 ± √5

Question 9

Given that z² - 10z + 25 = 9, what is z?

Solve using non Quadratic approach.

Answer 9

z² - 10z + 25 = 9

(z-5) (z-5) = 9 ⇒ Since left side of the quadratic is a

(z-5)² = 9 perfect square, factor left side first. √(z-5)² = √9 Leave the equation set to 9,

(z-5) = ± 3 dont change it to = 0 like

z= 5 ± 3 other quadratic.

z= 5+3 = 8; 5-3 = 2

Question 10

DS: What is x?

1) x = 4y-4
2) xy = 8

Answer 10

What is x? So this is a value question so there can only be 1 ans in order to be Suff

Each stmt alone is not enough info to solve for x. Using stmt 1 and 2 together, if you substitue the expression for x in the first equation into the second, you will get two different answers.

x = -8,4 Therefore, Ans is E. So be careful. Read the question carefully. Always ask yourself is the ques Value or Yes/NO. Ans will be diff if its Value or YES/NO question