Question

8 – 4x^3 + 4x^6 = 0,
state the number of complex roots, the possible number of real roots,and the possible rational roots.
@mathmale

Answer 1

I know there are 6 roots possible and 0 ,2 ,4 , or 6 real roots possible now i just need to find the possible rational roots

Answer 2

@Michele_Laino

Answer 3

@TheSmartOne

Answer 4

@phi

Answer 5

If you put the expression in standard order:
\[ 4x^6 – 4x^3+8= 0 \]
and count the number of sign changes
you get 2. that means there are either 2 or 0 positive real roots

if you put in -1 for x you get
4 +4 + 8 =0
and there are no sign reversals, so no negative real roots.

Answer 6

the possible answers are 1/8 1/4 1/2 1 2 4
or 1/4 1/2 1 2 4 8

Answer 7

the highest exponent is 6, so 6 complex roots
and either 2 or 0 real roots

Answer 8

ok i got that part but i have to find the possible rational roots

Answer 9

factors of 8 divided by factors of 4

Answer 10

the biggest possible rational root will be 8/1 = 8
the smallest 1/4

Answer 11

factors of 8 8 ,4,2,1
factors of 4 4,2,1

Answer 12

ok so 1/4 1/2 1 2 4 and 8?

Answer 13

yes

Answer 14

Thank you so much!!!!!!!