InterviewSolution
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InterviewSolution
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Statement -1 `ax^(3)+bx+c=0` where `a,b,c epsilonR` cannot have 3 non-negative real roots. Statement 2 Sum of roots is equal to zero.A. Statement -1 is true, Statement -2 is true, Statement -2 is a correct explanation for Statement-1B. Statement -1 is true, Statement -2 is true, Statement -2 is not a correct explanation for Statement -1C. Statement -1 is true, Statement -2 is falseD. Statement -1 is false, Statement -2 is true |
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Answer» Correct Answer - A Let `y=ax^(3)+bx+c` `:.(dy)/(dx)=3ax^(2)+b` For maximum or minimum `(dy)/(dx)=0` we get `x=+-sqrt(-b/(3a))` Case If `a gt0, bgt0` then `(dy)/(dx)gt0` In this case function is increasing so it has exactly one root Case II If `alt0, blt0` ten `(dy)/(dx)lt0` In this case function is decreasing so it has exactly one root. Case III `agt0, blt0` or `alo0, bgt0` then `y=ax^(3)+bx+c` is maximum at one point and minimum at other point. Hence all roots can never be non -netative. `:.` Statement -1 is false. But ltgtbrgt Sum of roots `=-("Coefficient of" x^(2))/("Coefficient of"x^(3))=0` i.e. Statement -2 is true. |
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