## anonymous 3 years ago find a quadratic equation having 3 + or - root 3 as roots

1. dan815

u want an equation with roots 3 or -sqrt3 ?

2. anonymous

no 3+/- sqrt3

3. dan815

ok

4. dan815

so work backwards from factor form

5. amistre64

when given a set of roots: {r1,r2,r3,...,rn} you can set up a poly by subtracting x from each root: (r1-x)(r2-x)(r3-x)...(rn-x)

6. dan815

oh wait u mean 3+/-root3

7. whpalmer4

@dan815 2 roots, this is a quadratic, so $$x= 3\pm\sqrt{3}$$

8. anonymous

yes

9. dan815

|dw:1371070589089:dw|

10. dan815

|dw:1371070608153:dw|

11. dan815

multiply em out and get ur equation

12. anonymous

ok thanks so much

13. amistre64

or $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $x=\frac{3\pm\sqrt{3}}{1}$ a = 1/2 b = -3 9-4c = 3 c = 6/4 $\frac12x^2-3x+\frac64$ $2x^2-12x+6$

14. amistre64

ugh ... i did a=1 in my determinant :/

15. amistre64

9-4c/2 = 3 9-2c = 3 c = 3

16. amistre64

1/2 x^2 -3x +3 x^2 -6x + 6 sounds better

17. anonymous

ok thank you!