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In copying a second-degree equation, the number without x was written as -30 in¬stead of 30. The answers found were 15 and -2. What are the answers of the correct problem? |
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Answer» ax2 + bx - 30 = 0. x = 15, 225a + 15b - 30 = 0 15a + b = 2 ...... 1 x = -2 4a - 2b - 30 = 0 2a - b = 15 .......2 (1) + (2) \(\rightarrow\) 17a = 17, a = 1 2 x 1 - b = 15 b = -13 Then the equation x2 - 13x - 30 = 0 Correct equation is x2 - 13x + 30 = 0 \(x=\frac{13\pm\,\sqrt{169-120}}{2},x=\frac{13\,\pm\,7}{2}\) \(x=\frac{13+7}{2}=10\) or \(\frac{13-7}{2}=3\) Solutions of the correct problem 10 or 3 |
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