Question

Suppose one of the roots of the polynomial function is irrational. The roots of the function are 2, √3, and 5. Write the equation for this polynomial function. Which of the following must also be a root of the function? a –2 b –√3 c –5 d √2

Answer 1

b. -√3

Explanation:

Given,

The roots of the polynomial function are 2 , √3 and 5,

Thus, the factors of the polynomial are (x-2), (x-√3) and (x-5),

Since, if (x-√a), where a is a real number, is a factor of a polynomial then (x+√a) is also a factor of the polynomial.

So, if (x-√3) is the factor of the given polynomial ⇒ (x-√3) is also the factor of the polynomial,

Hence, -√3 must be the root of the given polynomial.

Option 'b' is correct.

Answer 2

B

Explanation:

This is a good thing to put in mind. It is a simple enough question: I have never met a math teacher who wouldn't put it on a test. Best news of all, if you know the answer, it takes more time to indicate it than to get that answer.

Irrational roots (and complex ones) always come in pairs. There are no exceptions to this rule.

If one root is √3 then there is another one that is -√3. They both come from a binomial that looks like (x^2 - 3) which factors as (x + √3)(x - √3) and the zeros are √3 and -√3

Always. No exceptions.

So the answer is B