The discriminant if a quadratic equation is negative. One solution is 4 + 7i. What is the other solution? * 7 – 4i 4 – 7i

Question

The discriminant if a quadratic equation is negative. One solution is 4 + 7i. What is the other solution? *
7 – 4i
4 – 7i
– 4 + 7i
7 + 4i

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Ben Gia 3 years 2021-09-05T15:21:11+00:00 1 Answers 10 views 0

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  1. huyenthanh
    0
    2021-09-05T15:22:52+00:00
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    Answer:  B) 4 – 7i

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    Explanation:

    When you have a quadratic in the form ax^2 + bx + c = 0, where a,b,c are real numbers, then a negative discriminant leads to having a pair of complex roots. The roots come in conjugate pairs meaning that p+qi is one root while p-qi is the other root. The p,q are real numbers.

    In the case of 4+7i being one root, we have p = 4 and q = 7, since it matches with p+qi. The other root must be 4-7i since it matches with p-qi.

    In short, we flip the plus to a minus when going from 4+7i to 4-7i. All of this applies when we have a,b,c as real numbers.

    If we allowed a,b,c to be complex numbers, then the roots may not necessarily come in conjugate pairs.

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