SOLUTION: In this question the paper gives you a description and you're to put it into a quadratic equation.
The sum of the square of a number and 4 times the number is 12.
The equati
Question 78063: In this question the paper gives you a description and you're to put it into a quadratic equation.
The sum of the square of a number and 4 times the number is 12.
The equation I got was x^2+4x=12 I'm not sure if it's right but that's what I got. When I went to solve it though I didn't get what my teacher told me I would get, I didn't get two numbers in the end because the square root of the number I got was a decimal and she said we would get whole numbers. Can anyone help? Found 2 solutions by jim_thompson5910, scott8148:Answer by jim_thompson5910(35256) (Show Source):
In order to factor , first we need to ask ourselves: What two numbers multiply to -12 and add to 4? Lets find out by listing all of the possible factors of -12
Factors:
1,2,3,4,6,12,
-1,-2,-3,-4,-6,-12,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -12.
(-1)*(12)=-12
(-2)*(6)=-12
(-3)*(4)=-12
Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4
First Number
|
Second Number
|
Sum
1
|
-12
|
|
1+(-12)=-11
2
|
-6
|
|
2+(-6)=-4
3
|
-4
|
|
3+(-4)=-1
-1
|
12
|
|
(-1)+12=11
-2
|
6
|
|
(-2)+6=4
-3
|
4
|
|
(-3)+4=1
We can see from the table that -2 and 6 add to 4.So the two numbers that multiply to -12 and add to 4 are: -2 and 6
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=6
So the equation becomes:
(x-2)(x+6)
Notice that if we foil (x-2)(x+6) we get the quadratic again
So you get
Set each equation equal to zero and solve for x
or
So our solution is:
or
(