Question

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

• A. $ -4 $
• B. 1
• C. 4
• D. $ -\,2 $

Answer 1

The Correct Option is D

Since, $ \alpha $ and $ \beta $ are the roots of the equation $ a{{x}^{2}}+bx+c=0 $
$ \therefore $ $ \alpha +\beta =-\frac{b}{a} $ and $ \alpha \beta =\frac{c}{a} $
But $ \alpha \beta =3 $
$ \therefore $ $ 3=\frac{c}{a}\Rightarrow c=3a $ ...(i)
Also a, b, c are in AP.
$ \therefore $ $ b=\frac{a+c}{2} $
$ \Rightarrow $ $ b=\frac{a+3a}{2}=2a $ Hence, $ \alpha +\beta =-\frac{b}{a}=-\frac{2a}{a}=-2 $