Question

Find the roots of the polynomial equation. -x3 + 5x2 - 11x + 55 = 0

Answer 1

factor first two terms, and last terms separately

Answer 2

-x3 + 5x2 - 11x + 55 = 0
^ ^

Answer 3

Also, you can use the facts that the rational roots are the divisors of 55 so they are
\[
\pm1, \pm 5, \pm 11
\]
You find that the polynomial has a root x= 5, divide the polynomial by x-5 and you get the quotient then the answer.
The method suggested by @rsadhvika is easier.

Answer 4

Find the roots of the polynomial equation.

-x3 + 5x2 - 11x + 55 = 0

A.\[i \sqrt{11}\] ,\[-i \sqrt{11}\] , –5

B.\[\sqrt{11}\] ,\[-\sqrt{11}\] , 5

C.\[i \sqrt{11}\] , –5

D.\[i \sqrt{11}\] , \[-i \sqrt{11}\], 5

Answer 5

\[-x^3 + 5x^2 - 11x + 55 = 0\]
Perhaps this will help be a little more clear.

Answer 6

im thinking that it is D

Answer 7

why is that ? did u take time to read my or eliaasaab reply above ?

Answer 8

You shouldn't have to think, you should be able to know :-)

Answer 9

But yes, D is correct.

Answer 10

\[-(i\sqrt{11})^3+5(i\sqrt{11})^2-11(i\sqrt{11})+55\]\[= -11i^3\sqrt{11}+55i^2-11i\sqrt{11}+55\]\[=-11(-1)i\sqrt{11}+55(-1)-11i\sqrt{11}+55\]\[=11i\sqrt{11}-55-11i\sqrt{11}+55 = 0\]
conjugate root is similar

\[-(5)^3+5(5)^2-11(5)+55 = -125+125-55+55=0\]