Hi I have to find the sum and product of the roots of 3x^3+6x^2-2x+9. I'm having trouble finding the roots. I tried synthetic division, testing +/- 1,3,and 9 but none were zeroes. I don't know if I did this wrong. I also tried factoring but didn't get very far. I would appreciate any help. Thanks.
Sum & product of roots of a polynomial
- Thread starter xc630
- Start date
You didn't do anything wrong. Unfortunatly it doesn't have an integer solution nor even a nice fraction solution so synthetic doesn't work. You can go to
http://www.1728.com/cubic.htm
to find out what the answers are or go to
http://www.sosmath.com/algebra/factor/fac11/fac11.html
for a (very messy) longhand solution.
I don't know what they expected you to do. Are you sure you typed it correctly?
http://www.1728.com/cubic.htm
to find out what the answers are or go to
http://www.sosmath.com/algebra/factor/fac11/fac11.html
for a (very messy) longhand solution.
I don't know what they expected you to do. Are you sure you typed it correctly?
Hello, xc630!
I believe they expect you to know a theorem for this problem.
Given: .x<sup>3</sup> + ax<sup>2</sup> + bx + c .= .0 . . . Note: the leading coefficient is 1.
If the three roots are p, q, r, then:
. . . . .p + q + r .= .-a . . . the sum of the roots is the negative of a.
. . pq + qr + pr .= .b
. . . . . . . . .pqr .= .-c . . . the product of the roots is the negative of c.
Your equation is: .3x<sup>3</sup> + 6x<sup>2</sup> - 2x + 0 .= .0
Divide by 3: . x<sup>3</sup> + 2x<sup>2</sup> - (2/3)x + 3 .= .0
. . . . . .Sum of roots: . -2
. . . Product of roots: . -3
I believe they expect you to know a theorem for this problem.
In baby-talk, the theorem goes like this:
Given: .x<sup>3</sup> + ax<sup>2</sup> + bx + c .= .0 . . . Note: the leading coefficient is 1.
If the three roots are p, q, r, then:
. . . . .p + q + r .= .-a . . . the sum of the roots is the negative of a.
. . pq + qr + pr .= .b
. . . . . . . . .pqr .= .-c . . . the product of the roots is the negative of c.
Your equation is: .3x<sup>3</sup> + 6x<sup>2</sup> - 2x + 0 .= .0
Divide by 3: . x<sup>3</sup> + 2x<sup>2</sup> - (2/3)x + 3 .= .0
. . . . . .Sum of roots: . -2
. . . Product of roots: . -3
- Joined
- Feb 4, 2004
- Messages
- 16,583
Why do you need to find p, q, or r? Did the question ask you for that, or did it ask you for the sum and product of the roots? Did the previous post give you the formula (that your question assumed you'd learned) for the obtaining the sum and the product? And did the previous post also give you the answer to your question?
I'm sorry, but you've been provided the fully-worked solution. I'm not understanding what you still need.
Eliz.
I'm sorry, but you've been provided the fully-worked solution. I'm not understanding what you still need.
Eliz.