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if the difference between two roots of the equation x^3-13x^2+15x+189=0 is 2 then the difference between the greatest and the smallest roots is a)6 b)12 c)4 d)none

if the difference between two roots of the equation x^3-13x^2+15x+189=0 is 2 then the difference between the greatest and the smallest roots is    
a)6 b)12 c)4 d)none

Grade:10

1 Answers

Anusha Misra
26 Points
6 years ago
The given equation can be simplified to the form:
(x+3)(x-5)(x-7)=0
This means, x can take values, -3, 5 and 7.
The greatest root of the equation is then, 7
The smallest root of the equation, likewise, is -3
So the answer to the given question would be 7-(-3)=7+3=10.
 

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