InterviewSolution
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InterviewSolution
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Find all values of the parameter a for which the quadratic equation `(a+1)x^(2)+2(a+1)x+a-2=0` (i) has two distinct roots. (ii) has no roots. (iii) has to equal roots. |
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Answer» By the hypothesis, this equation is quadratic and therefore `a!=-1` and the discriminant of this equation `D=4(a+1)^(2)-4(a+1)(a-2)` `=4(a+1)(a+1-a+2)` `=12(a+1)` (i) For `agt(-1)` then `Dgt0`, this equation has two distinct roots. (ii) For `a lt(-1)`, then `Dlt0`, this equation has no roots. (iii) This equation cannot have two equal roots. Sicne, `D=0` only for `a=-1` and this contradicts the hypothesis. |
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