anonymous
  • anonymous
Which of the following is a polynomial with roots 4, 6, and −7?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
taramgrant0543664
  • taramgrant0543664
All you have to do is plug in each of the numbers for each equation if it equals zero it is a root
radar
  • radar
If you want the solution, work this out: Do the multiplication. (x-4)(x-6)(x+7)

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taramgrant0543664
  • taramgrant0543664
^^ that way is a lot easier both ways work though
anonymous
  • anonymous
multiply those three and thats the answer ?
taramgrant0543664
  • taramgrant0543664
If you expand it it will be your answer
anonymous
  • anonymous
wow thank you so much
radar
  • radar
Yes:|dw:1438394938481:dw|
anonymous
  • anonymous
is it x^3-24x^2-46x+168
taramgrant0543664
  • taramgrant0543664
I got x^3+7x^2-56x+168
mathmate
  • mathmate
The easiest way is to use the fact that the product of the three roots equals the negative of the constant term. So (4)(6)(-7)=-168. So look for the polynomial with -(-168)=168 as the constant term.
anonymous
  • anonymous
As mathmate said, for a cubic equation \[ax^3+bx^2+cx+d\] having roots \[\alpha,\beta,\gamma\] Use the following relation to quickly find the correct polynomial \[\alpha \times \beta \times \gamma = -\frac{d}{a}\]
anonymous
  • anonymous
When a=1, that is the coefficient of the cubic term, then it's simply equal to the negative of the constant term

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