Question
How many roots are real or complex? Does the polynomial 7+ 5x^4-3x^2 have in all
Answers
Answered by
GPT 3.5
The polynomial 7 + 5x^4 - 3x^2 has four terms. Since it is a fourth-degree polynomial, it can have a maximum of four roots, which may be real or complex.
To determine the number of real roots, we need to analyze the behavior of the function graph. The leading term is 5x^4, and as x approaches positive or negative infinity, the value of the function also approaches positive infinity. This means that the function has no real roots in this case.
Therefore, the polynomial 7 + 5x^4 - 3x^2 has no real roots, indicating that all four roots are complex.
To determine the number of real roots, we need to analyze the behavior of the function graph. The leading term is 5x^4, and as x approaches positive or negative infinity, the value of the function also approaches positive infinity. This means that the function has no real roots in this case.
Therefore, the polynomial 7 + 5x^4 - 3x^2 has no real roots, indicating that all four roots are complex.
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