Peg G.

asked • 10/03/17

writing a quadratic equation given the roots and the leading coefficient

Write the quadratic equation whose roots are 3 and -5, and whose leading coefficient is 3. 
(use the letter x to represent the variable)
 
Answer= _____   =0
I do know how to do the first half but I have trouble with the second half! Please help! Thanks in advance!
 
I do not know what to do after
3 (x-3)(x+5) 
What do you to get the next step?  

1 Expert Answer

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Kenneth S. answered • 10/03/17

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You're just asking for the last step.  The answer is to multiply it out.
Use FOIL to multiply the two binomials, then distribute the leading coefficient (3). DONE.
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Peg G.

okay, so when doing FOIL for this problem how do you do it? What are the numbers that you multiply (etc). I still don't understand how to FOIL this correctly.
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10/03/17

Kenneth S.

(a+b)(c+d) = (a+b)c + (a+b)d = c(a+b) + d(a+c) =ac + bc + ad + cd
 
THIS IS THE GENERAL RULE, PROVED.
 
FOIL tells you multiply the two 'firsties', then the two outer elements, then the two inners, and finally the two lasts:
F: ab
O: ad
I: bc
L: bd
 
When you do it, include the signs.
 
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10/03/17

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