SOLUTION: Find a quadratic equation that has solutions 5 and -6

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Question 149630: Find a quadratic equation that has solutions 5 and -6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!



Since 5 and -6 are given zeros this means that:


x=5 and x=-6


Get all terms to the left side in each case


x-5=0 and x%2B6=0


Now use the zero product property in reverse to join the factors.


%28x-5%29%28x%2B6%29=0


Expand and multiply

x%5E2%2Bx-30=0


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Answer:

So the polynomial with roots of 5 and -6 is

x%5E2%2Bx-30



Notice how if we graph y=x%5E2%2Bx-30, we can visually verify our answer

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2Bx-30+%29+ Graph of y=x%5E2%2Bx-30 with roots of x=5 and x=-6