Question

Information is given about a polynomial f left parenthesis x right parenthesis whose coefficients are real numbers. Find the remaining zeros of f. Degree​ 4; ​ zeros: i comma 5 plus i Enter the remaining zeros of f.

Answer 1

-i, 5-i

Explanation:

Given that a function f(x) has only real coefficients and also of degree 4.

Since any polynomial with real roots have imaginary roots only with conjugate pairs, we can find other two roots easily

Degree of polynomial = 4

No of roots = 4

GIven roots are i, 5+i

Conjugate of the given roots are -i, 5-i

Hence remaining zeroes of f are -i, 5-i

Answer 2

remaining zeros: negative i comma 5 minus i

Explanation:

The remaining two zeros are the conjugates of the two zeros given. That brings the total number to 4 zeros, consistent with the number of zeros expected for a 4th-degree polynomial.

The conjugate of a complex number has the same real part and the opposite imaginary part.