Find the simplest polynomial function with real coefficients that contains the roots 6 and .

Question

i need the answer to this question: Find the simplest polynomial function with real coefficients that contains the roots 6 and .
 

Answer 1

The complex root has the conjugate 3-4i. Combining the conjugates we get:

(x-3-4i)(x-3+4i)=x²-6x+9+16=x²-6x+25.

If we combine this with the factor x-6 we get the polynomial:

x³​​​​​​​-6x²+25x-6x²​​​​​​​+36x-150=x³-12x²​​​​​​​+61x-150.