Answers

1. 3 – √11  also be a root of f(x).

   What is Polynomial function ?

   A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

   According to the given Information:

   Get the conjugate of any irrational zero if you want rational coefficients.

   The conjugate of 3 + √11  is  3 – √11

   x = 3 +√ 11

   Subtract 3 on both sides

   x minus 3 = 3 + √11 – 3

   x – 3 = √11

   By squaring on both sides

   (x – 3)² =√ 11

   Now subtract 11 on both sides

   (x – 3)² – 11 = 0

   To factor use the difference of squares

   u² minus v² = (u minus v) (u plus v)

   [(x – 3) – 11][(x – 3) + 11] = 0

   We get,

   (x – 3) – 1 = 0 or (x – 3) + 11 = 0

   Solve for x – 3 and x

   Add √11 on both sides of first equation and subtract √11 on both sides of second equation

   x minus 3 = √11 or x minus 3 = – √11

   By adding 3 on both sides

   x = 3 + √11 or x = 3 – √11

   As a result,

   the root of 3 – √11 must likewise be f(x).

   To know more about Polynomial Function visit:

   https://brainly.com/question/2833285

   #SPJ4

   Reply
2. Answer:

     -3√11

   Step-by-step explanation:

   If the coefficients of a polynomial are rational, any irrational root will have a conjugate that is also a root.

   Irrational roots

   The root 3√11 is irrational, so its conjugate, -3√11, will also be a root.

   __

   Additional comments

   The conjugate of a root of the form a+√b or a+bi will be the same form with the sign changed: a-√b or a-bi.

   The conjugate of 3√11 = 0 +√99 will be 0 -√99 = -3√11.

   __

   A quadratic with rational coefficients can only have irrational roots of the form a±√b, where ‘a’ and ‘b’ may be any rational number.

   Reply