The cubic equation which have the roots 2, 3, 4 is
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x3 - 26x2 - 9x + 9 = 0
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x3 + 9x2 + 26x + 24 = 0
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x3 - 9x2 + 26x - 24 = 0
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x3 + 5x2 + 24 = 0
Reveal answer
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C
Correct answer
Explanation
Equation with roots 2, 3, 4 is (x-2)(x-3)(x-4) = 0. (x^2 - 5x + 6)(x-4) = x^3 - 4x^2 - 5x^2 + 20x + 6x - 24 = x^3 - 9x^2 + 26x - 24 = 0.
AI explanation
Using the factor form of a cubic polynomial, the required equation is (x - 2)(x - 3)(x - 4) = 0. Multiplying the first two factors gives x2 - 5x + 6, so the equation becomes (x2 - 5x + 6)(x - 4) = 0. Expanding this product yields x3 - 4x2 - 5x2 + 20x + 6x - 24 = 0, which simplifies to x3 - 9x2 + 26x - 24 = 0.