KVPY SX SB Exam 2012 Question Paper

Question : 5 of 120

Marks: +1, -0

Let a, b, c, d be numbers in the set {1,2,3,4,5,6} such that the curves

y = 2x^3 + ax + b

and

y = 2x^3+ c x + d

have no point in common. The maximum possible value of

( a -c )^2 + b - d

Solution:

y=2x^2+ax+b

y=2x^3+cx+d

No Solution

2x^3+ax+b≠2x^3+cx+d

ax+b≠cx+d

for no real x

(a-c)x≠d-b

x≠{d-b}/{a-c}

(a = c)

(a-c)^2+(b-d)

=0+6-1=5

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