Easy
If one root of $5x^2 + 13x + k = 0$ is the reciprocal of the other,then $k = $?
- A$0$
- B$5$
- C$1/6$
- D$6$
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If the product of roots of the equation $mx^2 + 6x + (2m - 1) = 0$ is $-1$,then the value of $m$ will be
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View SolutionIf the roots of the equation $Ax^2 + Bx + C = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + px + q = 0$ are $\alpha^2, \beta^2$,then the value of $p$ is:
Medium
View SolutionIf $\alpha, \beta$ are the roots of $a x^2+b x+c=0$,then the quadratic equation whose roots are $\sqrt{5} \alpha, \sqrt{5} \beta$ is
$\alpha, \beta, \gamma$ are the roots of the equation $x^3-10x^2+7x+8=0$. Match the following and choose the correct answer.
Column-$I$ Column-$II$ $A$. $\alpha+\beta+\gamma$ $(1)$ $-\frac{43}{4}$ $B$. $\alpha^2+\beta^2+\gamma^2$ $(2)$ $-\frac{7}{8}$ $C$. $\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}$ $(3)$ $86$ $D$. $\frac{\alpha}{\beta\gamma}+\frac{\beta}{\gamma\alpha}+\frac{\gamma}{\alpha\beta}$ $(4)$ $0$ $(5)$ $10$
| Column-$I$ | Column-$II$ |
| $A$. $\alpha+\beta+\gamma$ | $(1)$ $-\frac{43}{4}$ |
| $B$. $\alpha^2+\beta^2+\gamma^2$ | $(2)$ $-\frac{7}{8}$ |
| $C$. $\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}$ | $(3)$ $86$ |
| $D$. $\frac{\alpha}{\beta\gamma}+\frac{\beta}{\gamma\alpha}+\frac{\gamma}{\alpha\beta}$ | $(4)$ $0$ |
| $(5)$ $10$ |
DifficultTS EAMCET 2004
View SolutionIf one root of the equation $i x^2 - 2(i + 1) x + (2 - i) = 0$ is $(2 - i)$,then the other root is
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