Easy
The $H.M.$ between the roots of the equation $x^2 - 10x + 11 = 0$ is
- A$1/5$
- B$5/21$
- C$21/20$
- D$11/5$
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Similar Questions
If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$ ($a \neq 0$; $a, b, c \in \mathbb{R}$),then $(1 + \alpha + \alpha^2)(1 + \beta + \beta^2)$ is . . . .
Difficult
View SolutionIf in the equation $ax^2 + bx + c = 0$,the sum of roots is equal to the sum of the squares of their reciprocals,then $\frac{c}{a}, \frac{a}{b}, \frac{b}{c}$ are in
Difficult
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-$II$ |
| $(i) \alpha = \beta$ | $(A) (ac^2)^{1/3} + (a^2c)^{1/3} + b = 0$ |
| $(ii) \alpha = 2\beta$ | $(B) 2b^2 = 9ac$ |
| $(iii) \alpha = 3\beta$ | $(C) b^2 = 6ac$ |
| $(iv) \alpha = \beta^2$ | $(D) 3b^2 = 16ac$ |
| $(E) b^2 = 4ac$ | |
| $(F) (ac^2)^{1/3} + (a^2c)^{1/3} = b$ |
DifficultTS EAMCET 2008
View SolutionIf the ratio of the roots of the equation $12x^2 - mx + 5 = 0$ is $2 : 3$,then $m = .....$
Difficult
View SolutionIf the sum of the roots of the equation $\lambda x^2 + 2x + 3\lambda = 0$ is equal to their product,then $\lambda = $
Easy
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