Respuesta :
The zeros of the function f(x) = x⁴− x² − 2 are ±√2 or x = ±i option third positive or negative square root of 2, ±i is correct.
What is a complex number?
It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a function:
[tex]\rm f\left(x\right)=x^4-x^2-2[/tex]
Assume u = x²
[tex]\rm =u^2-u-2[/tex]
[tex]\rm =\left(u+1\right)\left(u-2\right)[/tex]
[tex]\rm =\left(x^2+1\right)\left(x^2-2\right)[/tex]
x = ±√2 or x² = -1 ⇒ x = ±i
Thus, the zeros of the function f(x) = x⁴− x² − 2 are ±√2 or x = ±i option third positive or negative square root of 2, ±i is correct.
Learn more about the complex number here:
brainly.com/question/10251853
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