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Algebra 2 help?
Hi I am so confused by this question. I've read the chapter but this isn't explained anywhere. Could someone please help? Also, if you know of a reliable website that would help me would you please link me to it?
Based on the Fundamental Theorem of Algebra, how many complex roots does each of the following equations have? Write your answer as a number in the space provided. For example, if there are twelve complex roots, type 12.
x(x2 - 4)(x2 + 16) = 0 has _____ a0 complex roots
(x 2 + 4)(x + 5)2 = 0 has _____ a1 complex roots
x6 - 4x5 - 24x2 + 10x - 3 = 0 has _____ a2 complex roots
x7 + 128 = 0 has _____ a3 complex roots
(x3 + 9)(x2 - 4) = 0 has _____ a4 complex roots
1 Answer
- JamesLv 47 years agoFavorite Answer
The number of complex roots is equal to the degree of the polynomial less the number of real roots.
For example, you see that the first equation is fifth degree and is in near complete factored form. Judging by the factors, there are three real roots x = 0, x = 2, and x = -2. These values cause the left side to equal zero.
However, there's no value for x in which (x^2 + 16) = 0. Therefore, there are two complex roots, which means the values for x in this case are not real numbers. Use the quadratic formula for this quadratic expression to see what we mean. You have a second degree polynomial with no real roots, leaving us with 2 complex roots.
Summary: When the factored form is attained, look for real values of x that can make the expression 0. Subtract the number of real roots from the degree of the polynomial to determine how many complex roots exist.
