Question

x^3 - x/2 -7 find the zero of the polynomial

Answer 1

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$x {}^{3 } - \frac{x}{2} - 1 = 0$

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$x {}^{3} - \frac{x}{2} - 7 = 0 \\ \frac{2x { }^{2 } - x - 14}{2} = 0 \\ 2x {}^{3} - x - 14 = 0 \\ add \: and \: subtract \: 4x {}^{2} \\ \\ 2x {}^{3} - 4x {}^{2} + 4x {}^{2} - x - 14 = 0 \\ \\ 2x {}^{3} - 4x {}^{2} + 4x {}^{2} - 8x + 7x - 14 = 0 \\ \\ 2x {}^{2} \times (x - 2) + 4x {}^{2} - 8x + 7x - 14 = 0 \\ \\ 2x {}^{2} \times (x - 2) + 4x \times (x - 2) + 7x - 14 = 0 \\ \\ 2x {}^{2} \times (x - 2) + 4x \times (x - 2) + 7(x - 2) = 0 \\ \\ (x - 2) \times (2x {}^{2} + 4x + 7) = 0 \\ \\ when \: the \: product \: equals \: 0 \: at \: least \: one \: factor \: is \: 0 \\ \\ x - 2 = 0 \\ 2x {}^{2} + 4x + 7 = 0 \\ \\ therefore \: x = 2$

hence the required answer will be 2.

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