Difficult
The equation $x^5-5x^3+5x^2-1=0$ has three equal roots. If $\alpha$ and $\beta$ are the other two roots of this equation,then $\alpha+\beta+\alpha\beta=$
- A$-4$
- B$3$
- C$-2$
- D$-5$
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If the sum of the roots of the equation $x^2 + px + q = 0$ is equal to the sum of their squares,then
Easy
View SolutionLet $\alpha$ and $\beta$ be the roots of the quadratic equation $a x^2+b x+c=0$. Match the conditions in List-$I$ with the corresponding relations in List-$II$.
List-$I$ List-$II$ $(i) \alpha = \beta$ $(A) (ac^2)^{1/3} + (a^2c)^{1/3} + b = 0$ $(ii) \alpha = 2\beta$ $(B) 2b^2 = 9ac$ $(iii) \alpha = 3\beta$ $(C) b^2 = 6ac$ $(iv) \alpha = \beta^2$ $(D) 3b^2 = 16ac$ $(E) b^2 = 4ac$ $(F) (ac^2)^{1/3} + (a^2c)^{1/3} = b$
| List-$I$ | List-$II$ |
| $(i) \alpha = \beta$ | $(A) (ac^2)^{1/3} + (a^2c)^{1/3} + b = 0$ |
| $(ii) \alpha = 2\beta$ | $(B) 2b^2 = 9ac$ |
| $(iii) \alpha = 3\beta$ | $(C) b^2 = 6ac$ |
| $(iv) \alpha = \beta^2$ | $(D) 3b^2 = 16ac$ |
| $(E) b^2 = 4ac$ | |
| $(F) (ac^2)^{1/3} + (a^2c)^{1/3} = b$ |
DifficultAP EAMCET 2008
View SolutionIf $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $ax^2 + bx + c = 0$,then:
Medium
View SolutionIf $\alpha, \beta$ are the roots of $(x - a)(x - b) = c$,where $c \neq 0$,then the roots of $(x - \alpha)(x - \beta) + c = 0$ are
If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4x+1=0$,then $(\alpha+\beta)^{-1}+(\beta+\gamma)^{-1}+(\gamma+\alpha)^{-1}$ is equal to
DifficultTS EAMCET 2003
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