Question

Degree 3 polynomial with zeros -7, 3i, and -3i

Answer 1

A polynomial having degree 3 with zeros -7, 3i, and -3i is:
x³+ 7x² - 9x - 63

The correct answer is an option (A)

In this question, we need to find the polynomial whose degree is 3 polynomial and zeros are -7, 3i, and -3i

The zeros of the required polynomial = -7, 3i, and -3i

This means, the roots of the polynomial = (x + 7), (x - 3i) and (x + 3i)

We know that in complex numbers, i = √-1

So, 3i = 3√-1

          = √-9

i.e., the roots of the polynomial are (x + 7), (x - √-9) and (x + √-9)

And the polynomial would be,

(x + 7)(x - √-9)(x + √-9)

= (x + 7)(x² - (√-9)²)

= (x + 7)(x² - (-9))

= (x + 7)(x² + 9)

=  x³+ 7x² - 9x - 63

Therefore, a polynomial having degree 3 with zeros -7, 3i, and -3i is:
x³+ 7x² - 9x - 63

The correct answer is an option (A)

Learn more about the polynomial here:

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