SOLUTION: Construct a polynomial given the information below: a second degree polynomial with zeros �2 and 5 and a constant term of �30

Question 821469: Construct a polynomial given the information below:
a second degree polynomial with zeros �2 and 5 and a constant term of �30
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
A general equation for a second degree polynomial in factored form would be:

where...
a = some non-zero constant
is one zero
is another zero

So for your polynomial we can write:

Simplifying...

Multiplying the last two factors:

Now we just have to figure out what number to use for "a". (I'll leave that part up to you.) Hint: Think about what number "a" needs to be in order for the constant term (without an x) to be -30 after you distribute the "a". If you can't figure out "a" from the above equation, then go ahead and distribute "a". Then figure out what number it needs to be to make the last term a -30. However you figure out the number for "a", replace "a" with that number and simplify (i.e. multiply).

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