SOLUTION: Sorry not sure what kind of algebra it is.
the question is from nov03 edexcel gcse paper, and tells us the area of a trapezium is 36cm^2
show that x^2-x-56=56, which i got to
Algebra ->
College
-> Linear Algebra
-> SOLUTION: Sorry not sure what kind of algebra it is.
the question is from nov03 edexcel gcse paper, and tells us the area of a trapezium is 36cm^2
show that x^2-x-56=56, which i got to
Log On
Question 77064: Sorry not sure what kind of algebra it is.
the question is from nov03 edexcel gcse paper, and tells us the area of a trapezium is 36cm^2
show that x^2-x-56=56, which i got to be,
1/2(a+b)h
=1/2(x+2+x+6)x-5
1/2(2x+8)x-5=36
x+4 multiplied by x-5
36 =x^2-20+4x-5
therefore x^2-x-56=0
is that right?
and then it asks you to solve the equation x^2-x-56=0
i've got so far
x^2-x=56
x^2=56+x
but i never know what to do next? please help! Answer by jim_thompson5910(35256) (Show Source):
In order to factor , first we need to ask ourselves: What two numbers multiply to -56 and add to -1? Lets find out by listing all of the possible factors of -56
Factors:
1,2,4,7,8,14,28,56,
-1,-2,-4,-7,-8,-14,-28,-56,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -56.
(-1)*(56)=-56
(-2)*(28)=-56
(-4)*(14)=-56
(-7)*(8)=-56
Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1
First Number
|
Second Number
|
Sum
1
|
-56
|
|
1+(-56)=-55
2
|
-28
|
|
2+(-28)=-26
4
|
-14
|
|
4+(-14)=-10
7
|
-8
|
|
7+(-8)=-1
-1
|
56
|
|
(-1)+56=55
-2
|
28
|
|
(-2)+28=26
-4
|
14
|
|
(-4)+14=10
-7
|
8
|
|
(-7)+8=1
We can see from the table that 7 and -8 add to -1.So the two numbers that multiply to -56 and add to -1 are: 7 and -8
Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:
substitute a=7 and b=-8
So the equation becomes:
(x+7)(x-8)
Notice that if we foil (x+7)(x-8) we get the quadratic again
Now set each factor equal to zero
So our answer is:
or
Since a negative answer doesn't work, the answer is
(