Question

http://i1142.photobucket.com/albums/n608/nancylam67/Page3664.jpg
do 4 only

Answer 1

thats easy , first find where derivative is zero

Answer 2

so you know where the function turns around ,

Answer 3

then compare the values of the function at the turning points

Answer 4

if you go from positive to negative , or negative to positive function value between two turning points then you must have an intersection with the x axis ( ie a zero )

Answer 5

if the sign of the function value doesnt change then there are no roots in the interval .

Answer 6

*no real roots

Answer 7

find the number of the real roots , then to find the number of complex root you subtract the number of real roots from the degree of the function

Answer 8

Or you can use Descartes theorem and count the sign changes in f(x) for positive roots and f(-x) for neg roots
positive: 2 or 4
negative: 1
imaginary: 0 or 2

Answer 9

no

Answer 10

By the fundamental theorem of algebra, this polynomial will have five roots.

Descartes rule of signs has that r has either two or zero positive real roots, and one negative real root.

The rational root theorem says that 1 is a root of r, and since this is real and positive, r clearly does not have zero real positive roots - it must have two.

So, we have so far:

Two real positive roots
One real negative root

Since r has rational coefficients, the remaining roots are complex conjugates by the complex conjugate root theorem.

So for r:

Two real, positive roots
One real, negative root
Two complex conjugate roots

Answer 11

thank all