InterviewSolution
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InterviewSolution
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If `x^2+p x+q=0a n dx^2+q x+p=0,(p!=q)`have a common roots, show that `p+q=0`. Also, show that their other roots are the roots of the equation `x^2+x+p q=0.` |
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Answer» Given equation are `x^(2) + px + q = 0` (1) and `x^(2) + qx + p = 0` (2) Clearly for x = 1, from both equations we get `1+ p + q = 0` . Also for (1), product of roots = q Therefore, (1) has roots x = 1 and x = q For (2), product of roots = p Therefoure, (2) has roots x = 1 and x = p Thus, the equation having roots p and q is `x^(2) - (p + q) x + pq = 0` `therefore x^(2) + x + pq = 0 (as 1 + p + q = 0 )` |
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