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A quadratic polynomial equation with real coefficients has a complex solution of the form a + bi with b ≠ 0. What

must its other solution be and why?

User Mmattax
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Answer: The other root of the given polynomial equation is a - bi, because complex roots always occur in conjugate pairs.

Step-by-step explanation: Given that a quadratic polynomial equation with real coefficients has a complex solution of the form a + bi with b ≠ 0.

We are given to find the a number that must be the other solution with reason.

We know that the complex roots of a quadratic equation always occur in conjugate pairs. That is,

if x + yi is one of the roots of a quadratic equation, then its conjugate x - yi is the other root of the equation.

According to this, we can say that the other root of the given quadratic polynomial is a - bi.

Thus, the other root of the given polynomial equation is a - bi, because complex roots always occur in conjugate pairs.

User AlexChaffee
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