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If the equation `x^(2) - 3x + b = 0` and `x^(3) - 4x^(2) + qx = 0`, where `b ne 0, q ne 0` have one common root and the second equation has two equal roots, then find the value of `(q + b)`. |
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Answer» Correct Answer - 6 `x^(2) - 3x + b = 0` ……(1) Let the roots are `alpha + beta`. `x^(3) - 4x^(2) + qx + 0`……(2) One root of the equation is zero and other root is repeated then roots are `0, beta, beta`, then Sum of roots `2beta = 4` `:. beta = 2` `alpha + beta = 3` by equation `(1)` `:. alpha = 1` `:. b = alphabeta = 2` `q = 0beta + beta^(2) + beta0 = beta^(2) = 4` `:. (b + q) = (2 + 4) = 6` |
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