If $\frac{3}{2} + \frac{7}{2}i$ is a solution of the equation $ax^{2} - 6x + b = 0$, where $a$ and $b$ are real numbers, then the value of $a + b$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
Let $\alpha = \frac{3}{2} + \frac{7}{2}i$
$\beta = \frac{3}{2} - \frac{7}{2}i$
$	herefore\ \ \alpha + \beta = 3,\ \ \ \alpha\beta = \frac{9}{4} + \frac{49}{4} = \frac{29}{2}$
$\Rightarrow \ \frac{6}{a} = 3,\ \frac{b}{a} = \frac{29}{2}$
$\Rightarrow \ \ a = 2,\ \ b = 29$
$\Rightarrow \ \ \ a + b = 31$

Q. If $\frac{3}{2} + \frac{7}{2}i$ is a solution of the equation $ax^{2} - 6x + b = 0$, where $a$ and $b$ are real numbers, then the value of $a + b$ is equal to

Explanation

Reviewed by Dr. Abubacker

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