Medium
If $\alpha, \beta, \gamma$ are the roots of $x^3+ax^2+bx+c=0$,then find the value of $\sum \frac{1}{\alpha}$,given that $\alpha, \beta, \gamma$ are non-zero.
- A$\frac{-b}{a}$
- B$\frac{b}{c}$
- C$\frac{-b}{c}$
- D$\frac{b}{a}$
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The equation formed by decreasing each root of $ax^2 + bx + c = 0$ by $1$ is $2x^2 + 8x + 2 = 0$. Then:
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View SolutionIf $\alpha, \beta \in \mathbb{R}$ are such that $1-2i$ (where $i^{2}=-1$) is a root of $z^{2}+\alpha z+\beta=0$,then $(\alpha-\beta)$ is equal to ..... .
$\alpha, \beta, \gamma$ are the roots of the equation $x^3-10 x^2+7 x+8=0$. Match the following and choose the correct answer.
$A. \alpha + \beta + \gamma$ $(1) -\frac{43}{4}$ $B. \alpha^2 + \beta^2 + \gamma^2$ $(2) -\frac{7}{8}$ $C. \frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}$ $(3) 86$ $D. \frac{\alpha}{\beta \gamma} + \frac{\beta}{\gamma \alpha} + \frac{\gamma}{\alpha \beta}$ $(4) 0$ $(5) 10$
| $A. \alpha + \beta + \gamma$ | $(1) -\frac{43}{4}$ |
| $B. \alpha^2 + \beta^2 + \gamma^2$ | $(2) -\frac{7}{8}$ |
| $C. \frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}$ | $(3) 86$ |
| $D. \frac{\alpha}{\beta \gamma} + \frac{\beta}{\gamma \alpha} + \frac{\gamma}{\alpha \beta}$ | $(4) 0$ |
| $(5) 10$ |
DifficultAP EAMCET 2004
View SolutionIf $\alpha$ and $\beta$ are the roots of the equation $4x^2 - \sqrt{13}x - 7 = 0$,then what is the value of $|\alpha - \beta|$?
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