Question

There are 4 different methods you could use to solve a quadratic equation that would depending upon the actual equation. They are: - factoring the equation - taking the square root of both sides - completing the square - using the quadratic formula In the two equations that are listed below, describe which method would be the most appropriate to determine a solution. Reference the parts of the equation to justify your response. (You do not have to solve the equation. Some words/phrases to consider using in your response would be:

- factor
- FOIL Method
- Zero-Product Property
- Standard Form
- quadratic expression
- quadratic equations
- coefficient
- perfect square
Part A: x^2 + 6x + 8 = 0
Part B: x^2 + 6x - 11 = 0

Answer 1

Part A - use the factor method

Part B - use the quadratic equation

Explanation:

Thinking process:

Let's look at the two parts in the problem:

Part A: x^2 + 6x + 8 = 0

This is a quadratic equation. Now, the product of the first and last term produces 8x². This product is a common multiple of 4 x and 2 x. These numbers can be added to get the middle term: 6x. Hence the equation can be solved by factorization.

Part B: x^2 + 6x - 11 = 0

Part B is also a quadratic equation. This equation can be analysed as follows:

The product of the first and last product gives -22x². Two factors are possibe: -11x and 2x or -2x and 11 x. These factors wjhen added or subtracted do not give the middle term (6x). Hence factorization will not work.

The best way to solve the equation is to use the quadratic formula:

`x= \frac{-b+/-\sqrt{b^(2)-4ac } }{2a}`

Answer 2

Part A: x^2 + 6x + 8 = 0 use the factoring the equation method

Part A: x^2 + 6x + 8 = 0 use the quadratic formula

Explanation:

Part A;

The equation is x^2 + 6x + 8 = 0 , looking at this quadratic expression, you notice it is written in a quadratic equation standard form of ax^2+bx+c=0. Additionally, you notice that can find what multiplied to get the quadratic equation,factor.You can identify two numbers that multiply to get ac and add to give b.In this question;

a=1,b=6,c=8

ac=8

The numbers are 4 and 2. Factoring the equation method will give;

x²+6x+8=0

x²+4x+2x+8=0

x(x+4)+2(x+4)=0

(x+2)+(x+4)=x²+6x+8

x+2=0, x=-2 and x+4=0, x=-4

Part B

The quadratic equation is ;

x²+6x-11=0

You notice that there are no factors that multiply direct to get the quadratic equation like in part 1. When you observe, a=1, b=6 and c=-11

ac=1×-11=-11 and b=6 .You notice there are no factors that multiply to give -11 and add to get 6, hence the factorizing the equation method can not be used.However, you can apply the quadratic formula that requires coefficients. You have a=1, b=c and c=-11 as the coefficients to use in the quadratic formula.