Q. The difference between two roots of the equation $x^{3} - 13x^{2} + 15x + 189 = 0$ is 2. Then the roots of the equation are
A) -3, 7, 9
B) -3, -7, -9
C) 3, -5, 7
D) -3, -7, 9
Explanation
(a)
Let roots of given equation are $\alpha,\ \alpha + 2$ and $\beta$
$\therefore\ \ \alpha + \alpha + 2 + \beta = 13$ ...(i)
$\alpha(\alpha + 2) + (\alpha + 2)\beta + \alpha\beta = 15$ ...(ii)
And $\alpha(\alpha + 2)\beta = - 189$ ...(iii)
These three equations are satisfies by the option (a)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.