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About Paul Klarreich
Expertise
I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction.
I can also try (but not guarantee) to answer questions on Abstract Algebra
-- groups, rings, etc. and Analysis -- sequences, limits, continuity.
I won't understand specialized engineering or business jargon.
Experience
I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
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You are here: Experts > Science > Mathematics > Advanced Math > Trigonometric equations
Expert: Paul Klarreich
Date: 5/10/2008
Subject: Trigonometric equations
Question
Find the sum of the roots tan^2x-9tan+1=0.
Do I factor? If so where do I start?
Answer
Questioner: Patrick
Category: Advanced Math
Private: No
Subject: Trigonometry
Question: Find the sum of the roots tan^2x-9tan+1=0.
Do I factor? If so where do I start?
...................................................
Hi, Patrick,
If you mean to treat your equation:
tan^2(x) - 9 tan(x) + 1 = 0.
simply as a quadratic, then the sum of the roots is 9. As far as factoring is concerned, forget it. You can't.
[formula: Sum = -b/a]
However, the roots are really the values of x. That's a bit more.
Apply the quadratic formula:
9 +- sqrt(81 - 4)
tan x = ------------------
2
9 +- sqrt(79)
tan x = --------------
2
Now you would work those out with your calculator, pressing the arctan (or inv tan) button at the end. Not exciting, and perhaps that is not what is meant, but it's the best I can do.
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