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If the equation x³-3x+a=0 has distict roots between 0&1 then the value of a is •2 •3 •½ •none of these (with method)

If the equation x³-3x+a=0 has distict roots between 0&1 then the value of a is


•2


•3


•½


•none of these


(with method)

Grade:12

4 Answers

Amit Jain
askIITians Faculty 32 Points
10 years ago
The sum of roots (let`s call them a, b ,c) will be -(-3) = 3. Now if the roots are distinct and between 0 and 1, there are no values of a,b,c which will satisfy above condition. So no such value of `a` would be possible. Amit Jain B.Tech IIT Delhi AskIITian Faculty
shubham sharma
27 Points
10 years ago
But here sum of roots is 0 !!
Amit Jain
askIITians Faculty 32 Points
10 years ago
Oh Yes!! I mistook the 3x term as 3x2. Very sorry for that. But that does not change the answer as the only possibility for a,b,c so that their sum is 0 is all of them equal to zero. But that will not comply with the term 3x as sum of roots taken two at a time. So again, no value of a is possible for this equation to have 3 distinct roots between 0 and 1. Again, apologies for the mistake. Amit Jain IIT Delhi
shubham sharma
27 Points
10 years ago
Ok thanks sir, I got other way to solve it around using differentiation!!!!

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