If $\alpha, \beta, \gamma$ are the roots of the equation $3 x^3-9 x^2+5 x-7$, then what is the value of…
If $\alpha, \beta, \gamma$ are the roots of the equation $3 x^3-9 x^2+5 x-7$, then what is the value of $\alpha+\beta+\gamma$ ?
- 3
- –3
- 9
- –9
Solution
Given,
$\alpha, \beta, \gamma$ are roots of $3 x^3-9 x^2+5 x-7=0$
$
\begin{aligned}
\therefore \quad \alpha+\beta+\gamma & =-\frac{b}{a} \\
& =\frac{-(-9)}{3} \\
\alpha+\beta+\gamma & =3
\end{aligned} \quad\left[\begin{array}{l}
\because a=3 \\
b=-9
\end{array}\right]
$
Hence, option (1) is correct
Asked in: AP EAMCET 2020 (22 Sep Shift 2)
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