AboutPaul Klarreich Expertise All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions.
I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.
Experience I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.
Question My name is Colleen. I am studying Pre-calculus. I am baffled by this problem. I have been trying to find a similar problem to use as as reference, but have not been successful. The problem is:
3 and i are two zeros of a cubis function. What is the third zero? Find a cubic funstion that has these three zeros.
I appreciate any guidance you can give!
Colleen
Answer Hi, Colleen,
You wrote:
Subject: Pre-Calculus
Question: My name is Colleen. I am studying Pre-calculus. I am baffled by this problem. I have been trying to find a similar problem to use as as reference, but have not been successful. The problem is:
3 and i are two zeros of a cubis function. What is the third zero? Find a cubic funstion that has these three zeros.
I appreciate any guidance you can give!
Colleen
-----------------
You FORGOT to write:
Find a cubic function WITH REAL COEFFICIENTS ...
That is critical. If the function has real coefficients, then imaginary roots, like x=i, must appear in conjugate pairs. Therefore, x = -i must also be a root. So the three roots are:
x = 3, x = i, x = -i.
And the three factors must be:
(x - 3)(x - i)(x + i)
Now the product of the second and third is x^2 + 1, so your polynomial is:
