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Form the polynomial equation whose roots are cubes of the roots of x3 + 3x2 + 2 = 0 |
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Answer» Given equation is x3 + 3x2 + 2 = 0 Put y = x3 so that x = y1/3 ∴ y + 3y2/3 + 2 = 0 3y2/3 = – (y + 2) Cubing on both sides, 27y2 = – (y + 2)3 = – (y3 + 6y2 + 12y + 8) ∴ y3 + 6y2 + 12y + 8 = 0 ⇒ y3 + 33y2 + 12y + 8 = 0 Required equation is x3 + 33x2 +12x +8= 0 |
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