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The sum of all the real roots of equation `x^4-3x^3-2x^2-3x+1=0` is |
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Answer» `x^4-3x^3-2x^2-3x+1 = 0` `(x^2-4x+1)(x^2+x+1) = 0` Now, roots of equation,`x^2-4x+1 = 0`, `x = (4+-sqrt(16-4))/2 = 2+-sqrt3` These are real roots. Now, roots of equation,`x^2+x+1 = 0`, `x = (-1+-sqrt(1-4))/2 = -(1+-sqrt(-3))/2` These are imaginary roots. `:.` Sum of real roots ` = (2+sqrt3)+(2-sqrt3) = 4` |
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