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What Is The Smallest Possible Value Of B? (JEE Main Question)

Sujoy Das
07/02/2018 0 0

Question:

Roots of the equation x^3 - ax^2 + bx - c = 0 are three consecutive integers then what is the smallest possible value of b?

A) -1/root3
B) -1
C) 0
D) 1
E) 1/root 3

 

Solution:

a-1, a and a+1

Min value of b = Min value of (a-1)a + a(a+1) + (a+1)(a-1)

= Min value of a^2 - a + a^2 + a + a^2 - 1

= Min value of 3a^2 - 1

= -1

 

y-1, y, y+1
b = (y-1)*y+(y-1)(y+1)+(y+1)*y = 3y^2-1.. minimum value -1

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