If $\alpha\$and $\beta$ are the roots of the equation $ax^{2} + bx + c = 0$, $\alpha\beta = 3$ and $a,\ b,\ c$ are in AP, then $\alpha + \beta$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
Here, $\alpha + \beta = - \frac{b}{a}$ and $\alpha\beta = \frac{c}{a}$
But $\alpha\beta = 3\ \ \  \Rightarrow \ \ \ \ c = 3a$
Also, $b = \frac{a + c}{2}\ \ \ \  \Rightarrow \ \ \ \ b = \frac{a + 3a}{2} = 2a$
Hence, $\alpha + \beta = - \frac{2a}{a} = - 2$

Q. If $\alpha\$and $\beta$ are the roots of the equation $ax^{2} + bx + c = 0$, $\alpha\beta = 3$ and $a,\ b,\ c$ are in AP, then $\alpha + \beta$ is equal to

Explanation

Reviewed by Dr. Abubacker

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