Question

A polynomial function P(x) with rational coefficients has the given roots find two additional roots of P(x)=0 i and 7+8i

Answer 1

Answer:

As, the given polynomial is P(x)=0,

It is given that two of it's roots are i and 7+ 8 i.

If this quadratic equation has four roots, there is no effect whether the powers of x has rational or any real coefficients.Why i have written this because imaginary roots or non real roots occur in pairs.

It is not necessary that this polynomial has only four roots, but number of non real root or imaginary root will be even.

So, if P(x)=0, has two roots → i and 7+ 8 i, other two roots will be -i and 7- 8 i.

Answer 2

Note that if a + bi is a root of P(x) = 0, then a – bi is also a root of P(x) = 0.

In this case, i and 7 + 8i are two roots of P(x) = 0. So –i and 7 – 8i are two additional roots of P(x) = 0.