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.
