Question

How many complex roots does the polynomial equation below have?

X^7-3x^5+4^2-1=0

Answer 1

4

Step-by-step explanation: 5 22 8 18 e

Graph the function and look for sign changes in the slope (easiest)

of the 7 roots 3 are real and 4 are complex

or the perferred way is to apply Descartes rule of signs

x^7-3x^5+4x^2-1=0 a typo in your function attached photos shows 4x²

(x^7) - (3x^5) +(4x^2) - (1) sign changes I see 3

then to find a bound on the number of negative roots

(-x^7) - (-3x^5) +(4x^2) - (1) = -x^7 + 3x^5 + 4x^2 - 1 I see 2 sign changes ??

there is at least 1 real root (due the odd highest power)

and either 0, 2, 4 or 6 complex roots

so 5 and 7 are out

still confused I used a polynomials root calculator

it said ther are three real roots (confirmed by the graph of the function)

and four comple roots (which I can't figure out from the graph)