Easy
If the sum of the roots of the equation $x^2 + px + q = 0$ is equal to the sum of their squares,then
- A$p^2 - q^2 = 0$
- B$p^2 + q^2 = 2q$
- C$p^2 + p = 2q$
- DNone of these
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If the roots of the equation $2x^2 - 3x + 5 = 0$ are the reciprocals of the roots of the equation $ax^2 + bx + 2 = 0$,then:
Easy
View Solution$\alpha, \beta, \gamma$ 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 $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3-13x^2+kx+189=0$ such that $\beta-\gamma=2$,then $\beta+\gamma: k+\alpha=$
If ${x^2} + px + 1$ is a factor of the expression $a{x^3} + bx + c$,then
DifficultIIT 1980
View SolutionThe two roots of the equation $x^3 - 9x^2 + 14x + 24 = 0$ are in the ratio $3 : 2$. Find the roots.
Difficult
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