Question

State how many imaginary and real zeros the function has.

f(x) = x4 - 8x3 + 17x2 - 8x +16

Answer 1

0 imaginary; 4 real

2 imaginary; 2 real

3 imaginary; 1 real

4 imaginary; 0 real

Answer 2

you can apply rational root test here - though my memory of it is a bit vague i'm afraid

as the last number is + 16 i would try x = 2 as 1 root

Answer 3

16 -64 + 68 - 16 + 16 = 0
yes x=2 is one root

Answer 4

i would venture to say that that might be a repeated root

Answer 5

because of the coefficients in the equation

Answer 6

So 2 imaginary and 2 real?

Answer 7

maybe 4 real

Answer 8

So four real and zero imaginary?

Answer 9

i'm not absolutely sure - I'd have to revise this stuff sorry i cant be of any more help

Answer 10

Thanks anyway

Answer 11

i'm sure there are 2 real roots - both = 2
so its either option 1 or option 2

Answer 12

yw

Answer 13

I'll go with the first one and see what happens. Thanks :)

Answer 14

I've looked at this again. I made an error - the root is not 2 but 4.
applying Descartes rule of signs there is either 0,2 or 4 real positive roots and no real negative roots. But we have found one real positive root which is 4. I suspected that this is a double root so did a long division .
If 4 is a double root then the polynomial is divisible by (x-4)^2 or
x^2 - 8x + 16

- which it is and the quotient is x^2 + 1 which if you equate to zero gives 2 imaginary roots i and -i
so the correct option is B, 2 imaginary and 2 real