SOLUTION: How many complex roots does the polynomial equation have? 5x^3 - 4x + 1 = 0 A. 2 B. 3 C. 4 D. 5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How many complex roots does the polynomial equation have? 5x^3 - 4x + 1 = 0 A. 2 B. 3 C. 4 D. 5      Log On


   



Question 1127571: How many complex roots does the polynomial equation have?
5x^3 - 4x + 1 = 0

A. 2
B. 3
C. 4
D. 5

Found 2 solutions by math_helper, Alan3354:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+highlight%28matrix%281%2C3%2C+%22B.%22%2C+%22+%22%2C+%22+3%22%29+%29+


The number of roots matches the highest degree of x.

The roots are:
+-1++

+1%2F2+-+1%2F%282%2Asqrt%285%29%29+++

+1%2F2+%2B+1%2F%282%2Asqrt%285%29%29++

These are the three complex roots. They happen to all be real numbers, but a real number is simply a complex number with imaginary part = 0 (so we can write -1 = -1 + 0i, etc.).
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EDIT: Commenting on Alan3354's answer: "non-real" roots (roots whose imaginary components are nonzero) come in conjugate pairs. We have only real roots and those real roots are also complex numbers (with imaginary component equal to zero). Student: You may read about "complex" roots coming in conjugate pairs, but when you see that, remember they really mean "non-real" roots.


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How many complex roots does the polynomial equation have?
5x^3 - 4x + 1 = 0
==========
it's a cubic, so there are 3 roots.
Complex roots occur in pairs --> an even number.
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2