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tan 3xFor what integral values of a, the equation x -x(1 - a) (a2) 0 has integral roots.Find the roots2 |
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Answer» This is a quadratic equation. It will have integral roots when: b2 - 4ac = 0 a = 1 ; b = - ( 1 - a ) ; c = - ( a + 2) ( - 1 + a )2 - 4 (1) ( -a - 2) = 0 1 - 2a + a2 + 4a + 8 = 0 a2 + 2a + 9 = 0 This is a parabola that lies completely above the x-axis, therefor it willnot have real roots (integral roots)There are no integral values of a which satisfy this equation! Algebraically: completing the square ( a + 1 )2 = - 9 + 1 ( a + 1)2 = -8 a + 1 = √ -8 a = -1 + √ -8 This will not be an integral value If all of your numbers and signs are correct, this is what I get. |
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