Reading the answer properly for roots

I have a polynomial

     p(x) = (x^5 + 1.3301x^4 - 9.1234x^3 + 1)(x^2 - 9976/1000)

I need to find the roots preferably to the nearest 100,000th.

Here is what I do:

    p = [1 1.3301 -9.1234 0 0 1]; roots(p);

my result is:

    -3.760932681080143 + 0.000000000000000i
    2.416314783767116 + 0.000000000000000i
    0.495523859135796 + 0.000000000000000i
    -0.240502980911384 + 0.405248700488689i
    -0.240502980911384 - 0.405248700488689i

then I do:

    p = [1 0 9976/1000]; roots(p);

my result is:

    -0.000000000000000 + 3.158480647399949i
    0.000000000000000 - 3.158480647399949i

I'm not really understanding my answers or if they are even correct. If someone could explain them I would appreciate it.

Answer 1

[Walter Roberson]

Those look correct. The "i" (lower-case I) at the end of numbers indicates the imaginary component. So one of the solutions is

-3.760932681080143 + 0.000000000000000i

which has an imaginary component of 0 and so could be written more typically as

-3.760932681080143

but

-0.240502980911384 + 0.405248700488689i

has both real and imaginary components.

[ImNew Matlab]

Thank you, what exactly is an imaginary component? and in this case would "-0.240502980911384" be a real root? If so why are they listed together in one row instead of separated?

[Walter Roberson]

"i" at the end should be read as "* sqrt(-1)", so one of the roots is

-0.240502980911384 + (0.405248700488689 * sqrt(-1))

In that expression, -0.240502980911384 is only the real component of the number, and is not a root in itself.