The difference between two roots of the equation $x^3-13 x^2+15 x+189=0$ is 2 . Then the roots of the…
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 :
$-3,5,7$
$-3,-7,-9$
$3,-5,7$
$-3,-7,9$
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).