Q75 / 160 · AP EAMCET 2020 (22 Sep Shift 2) · Mathematics

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 $\alpha+\beta+\gamma$ ?

  • Correct answer
    A
    3
  • B
    –3
  • C
    9
  • D
    –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.

Hence, the correct answer is option: 'A'.

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