If you know a root of a function is -2 + the square root of 3i then 2 + the square root of 3i is a possible root. 2 + the square root of 3i is a known root. -2 - the square root of 3i is a possible root. -2 - the square root of 3i is a known root. just finished the assignment got it wrong but the correct answer is -2 - the square root of 3i is a known root

-2 - the square root of 3i is a known root

Step-by-step explanation:

we know that

The conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial

we have that

The root of a function is

so

Applying the conjugate root theorem

---> is also a root of the function

therefore

-2 - the square root of 3i is a known root

7.6 m/s faster

Step-by-step explanation:

Speed of swimmer = 1.8 meters per second

The distance covered by runner = 200

Time of runner = 21.3 sec

We have to find the speed of the runner first so that we can compare with the speed of swimmer.

Speed = Distance/Time

=> 200/21.3

=> 9.4 m/s

So we have to find the difference between both speeds

Difference = 9.4 - 1.8

=> 7.6 m/s

So the runner was 7.6 m/s faster..