Question

a polynomial function with rational coefficients has the given roots. find two additional roots -2i and square root of 10

Answer 1

Answer:

(-2)(100) or 10^2 is 100

Step-by-step explanation:

(x -2)(x+100) =x

Answer 2

Additional roots of polynomial function P(x) with rational coefficients are (2i) and (- √10).

What is conjugate of complex number?

" If z = a +bi be the given complex number, then its conjugate is represented by $\bar{z}$ = a -bi , where  real parts remain same only imaginary part  get changed with opposite sign."

Theorem used

Conjugate Root theorem

Complex conjugate root theorem states that if P(x) is a polynomial in one variable with real coefficient , for P(x) if one root is a + bi  with real numbers a and b then its conjugate that is a - bi is also another additional root of P(x).

According to the question,

Two given roots of polynomial function with rational coefficients are -2i and √10.

As per Conjugate root theorem,

Here one root is 0 - 2i then other root is its conjugate 0 + 2i

Also one root is 0 + √10 then another root is 0 - √10.

Therefore, two additional roots are 2i and -√10.

Hence, additional roots of polynomial function P(x) with rational coefficients are (2i) and   (- √10).

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