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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