SOLUTION: 1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. Answer: Show work in this space. b) Solve by using the quadratic

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Question 76350: 1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks:
a) Solve by factoring.
Answer:
Show work in this space.

b) Solve by using the quadratic formula.
Answer:
Show work in this space.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
a)
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to 8 and add to -6? Lets find out by listing all of the possible factors of 8


Factors:

1,2,4,8,

-1,-2,-4,-8,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 8.

1*8=8

2*4=8

(-1)*(-8)=8

(-2)*(-4)=8

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6

||||
First Number|Second Number|Sum
1|8|1+8=9
2|4|2+4=6
-1|-8|-1+(-8)=-9
-2|-4|-2+(-4)=-6
We can see from the table that -2 and -4 add to -6.So the two numbers that multiply to 8 and add to -6 are: -2 and -4 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: substitute a=-2 and b=-4 So the equation becomes: (x-2)(x-4) Notice that if we foil (x-2)(x-4) we get the quadratic again

So in other words, factors to
Now set each factor equal to zero:

Solve for x

Solve for x
So our solution is x=2 and x=4




b)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4, 2. Here's your graph:

So our solution is x=2, and x=4.
Notice how we got the same answer but took another route to get there.
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