Q55 / 160 · AP EAMCET 2006 · Mathematics

The difference between two roots of the equation $x^3-13 x^2+15 x+189=0$ is 2 . Then the roots of the equation are :

  • Correct answer
    A
    $-3,5,7$
  • B
    $-3,-7,-9$
  • C
    $3,-5,7$
  • D
    $-3,-7,9$

Solution

Let roots of the equation $x^3-13 x^2+15 x+189=0$ are $\alpha, \alpha+2$ and $\beta$ $\alpha+\alpha+2+\beta=13$ $\ldots$ (i) $\alpha(\alpha+2)+(\alpha+2) \beta+\alpha \beta=15$ $\ldots$ (ii) and $\quad \alpha(\alpha+2) \beta=-189$ $\ldots$ (iii) These three equations are satisfied by the option (a).

Hence, the correct answer is option: 'A'.

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