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Let a, b, c, d be numbers in set {1, 2, ...

Let a, b, c, d be numbers in set {1, 2, 3, 4, 5, 6} such that the curves `y=2x^(3)+ax+b` and `y=2x^(3)+cx+d` have no point in common. The maximum possible value of `(a-c)^(2)+b-d` is-

A

0

B

5

C

30

D

36

Text Solution

Verified by Experts

The correct Answer is:
B
`y = 2x^(3)+ax+b" "y=2x^(3)+cx+d`
No solution
`2x^(3)+ax+bne2x^(3)+cx+d`
`ax+bnecx+d" for no real x"`
`(a-c)xned-b`
`xne(d-b)/(a-c)" "a = c"`
`(a-c)^(2)+(b-d)=0+6-1=5`
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