Two roots of a 3-degree polynomial equation are 5 and -5. which of the following cannot be the third root of the equation?
there are multiple answers.
5
5i
0
-5
-5i

Option 2 and 5.

Step-by-step explanation:

It is given that two roots of a 3-degree polynomial equation are 5 and -5.

The number of roots is equal to the degree of the polynomial.

Degree of the polynomial is 3 it means the number of roots is 3.

According to the complex conjugate root theorem if a complex number a+ib is a root of polynomial P(x) then its conjugate a-ib is also the root of P(x). It means the number of complex root is always even.

Two given roots are real, so the remaining single root must be a real number.

So, 5i and -5i can not be the third root of the equation.

Therefore, the correct options are 2 and 5.

$12. that is my answer.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)