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Question

Which of the following could be the possible integral value(s) of 'a' for which the equation x33x+a=0 has three distinct roots?

A
1
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B
-1
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C
0.0
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D
3
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E
-3
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Solution

The correct options are
A 1
B -1
C 0.0
Letf(x)=x33x+aLet f'(x)=03x23=0x=±1For three distinct real roots,f(1)f(1)<0(13+a)(1+3+a)<0(a+2)(a2)<02<a<2Possible values of a are 1, 0, 1.

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