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Given the function, where a, b, and c are positive numbers:
f(x) = (x - a)(x - b)2(x2 + c)
How many real roots does f(x) have, including multiple roots? |
How many imaginary roots does f(x) have?

Sagot :

Answer:

2 real roots and 1 imaginary roots

Step-by-step explanation:

f(x) = [tex](x-a)(x-b)^{2} (x^{2}+c)[/tex]

There are only 2 real roots and one imaginary roots.

Separate the equation into sections because the function is a multiplication with no outside sum or substraction:

Real Roots:

[tex](x-a)[/tex] = 0 when x = a

[tex](x-b)^{2}[/tex] = 0 when x = b

Imaginary roots:

[tex](x^{2}-c)[/tex] = 0 when x = [tex]\sqrt{-c}[/tex]

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