If a polynomial function, f(x), with rational coefficients has roots 0, 4, and 3 startroot 11 endroot, what must also be a root of f(x)?

Answers

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 firstequation and subtract √11 on both sides of second equation

3 – √11also be arootof f(x).What is Polynomial function ?polynomial function is a function that involves onlynon-negative integerpowers or only positive integerexponentsof avariablein an equation like the quadratic equation, cubic equation, etc.## According to the given Information:

irrationalzero if you want rational coefficients.firstequationand subtract √11 on both sides ofsecond equationPolynomial Functionvisit:#SPJ4Answer:Step-by-step explanation:coefficientsof a polynomial arerational, anyirrational rootwill have aconjugatethat is also a root.## Irrational roots

-3√11, will also be a root.Additional comments