State the degree of the following polynomial equation. Find all of the real and

Question

State the degree of the following polynomial equation. Find all of the real and imaginary roots of the equation, stating multiplicity when it is greeter than on x-10x 0 (Type a whole number. Find the real rational roots, if any. Select the correct choice below, and if necessary, fill in the answer box to complete your choice. OA One real rational root isand the other real rational root with multiplity 2 is OB. Temal rational root(s) is/are OC. The real rational root is with multiplicity 3. 0 D. There are no real rational roots. Find the real irrational roots, if any. Select the correct choice below, and if necessary, fill in the answer box to complete your choice. OA one real imatinal root isand the other real irrational root with multiplicity 2 is O B. The real irrational root(s) is/are Type integers or simplified fractions.) Type an integer or a simplified fraction. Use a comma to separate answers as needed.) Type an integer or a simplified fraction.) (Simplify your answers. Type exact answers, using radicals as needed.) (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) C. The real irrational root is with multiplicity O D. There are no real irrational roots Find the imaginary roots, if any. Select the correct choice below, and if necessary, fill in the answer box to complete your choice 3. (Simplify your answer. Type an exact answer, using radicals as needed.) A. The imaginary root(s) is/are (Simplify your answer. Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.) There are no imaginary roots. 0 B. Click to select your answer(s).

Explanation / Answer

x^3 - 4x^2 - 10x = 0

x ( x^2 - 4x - 10 ) = 0

x = 0

x = ( 4 +- sqrt ( 16 + 40 ) ) / 2

x = 2+ sqrt 14 , 2 - sqrt 14

the real rational root is 0

b) the real irrational roots are

( 2 + sqrt 14 , 2 - sqrt 14 )

c) there are no imaginary roots

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