# Math problem, did I do it right. **URL:** \ **Category:** Factual Questions\ **Created:** [September 24, 2009, 6:07pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401 "2009-09-24T18:07:13Z")\ **Posts on this page:** 11\ **Page:** 1
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [September 24, 2009, 6:07pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/1 "2009-09-24T18:07:13Z")
I am really iffy as to this problem. One solution to a quadratic equation is “1-3i”. The coeffecients of the equations terms are rational. What is the constant term when the equation is in standard form. The solution I got is x^2 + 2 x + 10 = 0. Constant term is 10 ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [September 24, 2009, 6:11pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/2 "2009-09-24T18:11:52Z")
That’s right, but for questions like these it’s always a good idea to post your logic so that if you don’t have the right answer we can help you to find your mistakes. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [September 24, 2009, 6:36pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/3 "2009-09-24T18:36:01Z")
Your 10 is correct, but in your polynomial, the coefficient of x should be -2, not 2. ---
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [September 24, 2009, 6:40pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/4 "2009-09-24T18:40:37Z")
Thanks ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [September 24, 2009, 6:48pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/5 "2009-09-24T18:48:55Z")
Generally, if one solution to a quadratic with real terms is a + bi (with a and b real), the other solution is a - bi. So the two solutions must be 1 ± 3i, and the polynomial must be: (x - 1 - 3i)(x - 1 + 3i) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 24, 2009, 8:56pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/6 "2009-09-24T20:56:00Z")
> [@](#): > > Generally, if one solution to a quadratic with real terms is a + bi (with a and b real), the other solution is a - bi. To clarify this, **Giles** is using the mathematical definition of “generally” here. That’s not “It’s a pretty good bet that the other solution is probably a-bi”, that’s “In all cases and under all circumstances subject to the stated conditions, the other solution is always a-bi”. ---
**Author:** ![JWT\_Kottekoe](https://avatars.discourse-cdn.com/v4/letter/j/3ec8ea/32.png) [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)\ **Post date:** [September 25, 2009, 1:47am UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/7 "2009-09-25T01:47:52Z")
> [@Chronos](#): > > In all cases and under all circumstances subject to the stated conditions Which is easily seen to be true: Since the equation has real coefficients, its complex conjugate is the same equation, and thus, if X is a solution, its complex conjugate must also be a solution. ---
**Author:** ![Tyrrell\_McAllister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tyrrell_mcallister/32/16772_2.png) [@Tyrrell\_McAllister](https://boards.straightdope.com/u/Tyrrell_McAllister)\ **Post date:** [September 25, 2009, 2:15am UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/8 "2009-09-25T02:15:00Z")
> [@JWT\_Kottekoe](#): > > Which is easily seen to be true: Since the equation has real coefficients, its complex conjugate is the same equation, and thus, if X is a solution, its complex conjugate must also be a solution. …easily seen once you check that complex conjugation respects multiplication. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [September 25, 2009, 9:55pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/9 "2009-09-25T21:55:28Z")
However, unless you specify that the leading coefficient is 1, there is no unizue solution. If the equation is x^2 - 2x +10 =0, then 2x^2 -4x - 20 has the same roots. ---
**Author:** ![Blaster\_Master](https://avatars.discourse-cdn.com/v4/letter/b/cab0a1/32.png) [@Blaster\_Master](https://boards.straightdope.com/u/Blaster_Master)\ **Post date:** [September 25, 2009, 10:03pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/10 "2009-09-25T22:03:56Z")
> [@Hari\_Seldon](#): > > However, unless you specify that the leading coefficient is 1, there is no unizue solution. If the equation is x^2 - 2x +10 =0, then 2x^2 -4x - 20 has the same roots. Except the problem does specify that the constant term is 10, so the second solution doesn’t fit the problem. ---
**Author:** ![Tyrrell\_McAllister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tyrrell_mcallister/32/16772_2.png) [@Tyrrell\_McAllister](https://boards.straightdope.com/u/Tyrrell_McAllister)\ **Post date:** [September 25, 2009, 10:14pm UTC](https://boards.straightdope.com/t/math-problem-did-i-do-it-right/511401/11 "2009-09-25T22:14:10Z")
That the constant term is 10 is the _answer_ to the problem, not a given piece of information. However, it is given that the polynomial is to be in “standard form”, which I expect means that the leading coefficient is to be 1.