Find the area of a rectangle with length (2x + 3) and width (x - 4). A) 2x2 - 11x - 12 B) 2x2 - 5x + 12 C) 2x2 + 11x + 12 D) 2x2
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Answer: The required polynomial of lowest degree is
Step-by-step explanation: We are given to find a polynomial function of lowest degree with real coefficients having zeroes of 2 and -5i.
We know that
if x = a is a zero of a real polynomial function p(x), then (x - a) is a factor of the polynomial p(x).
So, according to the given information, (x - 2) and ( x + 5i) are the factors of the given polynomial.
Also, we know that complex zeroes occur in conjugate pairs, so 5i will also be a zero of the given polynomial.
This implies that (x - 5i) is also a factor of the given polynomial.
Therefore, the polynomial of lowest degree (three) with real coefficients having zeroes of 2 and -5i is given by
Thus, the required polynomial of lowest degree is