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In-s [12.5K]
3 years ago
15

Need help!!!!!!!!!!!!!!

Mathematics
1 answer:
Alenkinab [10]3 years ago
6 0
50.24 multiply 3.14 by 16
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Which correctly describes the roots of the following cubic equation x^3-5x^2+3x+9=0? A. Three real roots, each with a different
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Answer:

The correct option is C.

Step-by-step explanation:

The given cubic equation is

x^3-5x^2+3x+9=0

According to the rational root theorem 1 and -1 are possible rational roots of all polynomial.

At x=-1, the value of function 0. Therefore (x+1) is the factor of polynomial and -1 is a real root.

Use synthetic division to find the remaining polynomial.

(x+1)(x^2-6x+9)=0

(x+1)(x^2-2(3)x+3^2)=0

Using (a-b)^2=a^2-2ab+b^2

(x+1)(x-3)^2)=0

USe zero product property and equate each factor equal to 0.

x=-1,x=3,x=3

Therefore the equation have three real roots out of which the value of two roots are same.

Option C is correct.

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