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Section 2.2
Question 66
Can you solve 66 as a guide for me to do a few more?
Question 66
Can you solve 66 as a guide for me to do a few more?
66.
x=-2,6
to find a polynomial use zero product rule
since given two roots, x[1]=-2 and x[2]=6, you need
f(x)=(x-x[1])(x-x[2])
f(x)=(x-(-2))(x-6)
f(x)=(x+2)(x-6)
f(x)=x^2 - 4x - 12-> your polynomial
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The "Zero Product Property" says that:
If a *b = 0 then a = 0 or b = 0 (or both a=0 and b=0).
It can help us solve equations:
Example: Solve (x−5)(x−3) = 0
The "Zero Product Property" says:
example:
If (x−5)(x−3) = 0 then (x−5) = 0 or (x−3) = 0
Now we just solve each of those:
For (x−5) = 0 we get x = 5
For (x−3) = 0 we get x = 3
And the solutions are: x = 5, or x = 3
Here it is on a graph:
View attachment 338
y=0 when x=3 or x=5
another example:
3(x - 2) = 3x(x - 2)
Use "Standard Form":
3(x - 2) - 3x(x - 2) = 0...........factor completely
Which can be simplified to:
(3 - 3x)(x - 2) = 0
or 3(1 - x)(x - 2) = 0 ...........where 3, (1 - x) and (x - 2) are factors
Then the "Zero Product Property" says:
since 3>0, then zeros are x values that makes
(1 - x) = 0, or (x - 2) = 0
so, x = 1 or x = 2