## anonymous one year ago Which of the following is a polynomial with roots 4, 6, and −7?

1. anonymous

2. taramgrant0543664

All you have to do is plug in each of the numbers for each equation if it equals zero it is a root

If you want the solution, work this out: Do the multiplication. (x-4)(x-6)(x+7)

4. taramgrant0543664

^^ that way is a lot easier both ways work though

5. anonymous

multiply those three and thats the answer ?

6. taramgrant0543664

7. anonymous

wow thank you so much

Yes:|dw:1438394938481:dw|

9. anonymous

is it x^3-24x^2-46x+168

10. taramgrant0543664

I got x^3+7x^2-56x+168

11. 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.

12. 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 $\alpha \times \beta \times \gamma = -\frac{d}{a}$

13. anonymous

When a=1, that is the coefficient of the cubic term, then it's simply equal to the negative of the constant term