Respuesta :
The f(x) has three real roots and two imaginary roots option (D) is correct.
What is polynomial?
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial:
f(x) = x⁵ − 8x⁴ + 21x³ − 12x² − 22x + 20
The three roots of this polynomial function are −1, 1, and 3 + i.
We can write the function in a factored form:
f(x) = (x - 1)(x⁴ - 7x³ + 14x² +2x - 20)
Again factoring the above polynomial:
f(x) = (x - 1)(x + 1)(x - 2)(x² -6x + 10)
The roots of the polynomial are
x - 1 = 0
x = 1
x + 1 = 0
x = -1
x - 2 = 0
x = 2
x² - 6x + 10 = 0
The above quadratic equation has two complex roots.
x = 3 + i
x = 3 - i
Thus, the f(x) has three real roots and two imaginary roots option (D) is correct.
Learn more about Polynomial here:
brainly.com/question/17822016
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