InterviewSolution
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InterviewSolution
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The number of value of `k`for which `[x^2-(k-2)x+k^2]xx""[x^2+k x+(2k-1)]`is a perfect square is`2`b. `1`c. `0`d. none of theseA. 2B. 1C. 0D. none of these |
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Answer» Correct Answer - 2 For given situation, `x^(2) - (k - 2)x + k^(2) = 0 and x^(2) + kx + 2k - 1 = 0` should have both roots common or each should have equal roots. If both roots are common, then `1/1 = (-(k - 1))/(k) = (k^(2))/(2k - 1)` `rArr k = -k + 2 and 2k - 1 = k^(2) rArr k = 1` If both the equations have equal roots, then `(k - 2)^(2) - 4k^(2) = 0 and k^(2) - 4(2k - 1) = 0` `rArr (3k - 2) (-k - 2) = 0 and k^(2) - 8k + 4 = 0` There is no common value of k. Therefore, k = 1 is the only possible value. |
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