The equation whose roots are those of equation $x^{4} - 3 x^{3} + 5 x^{2} - 2 = 0$ with contrary sign is

x^{4} + 3 x^{3} + 5 x^{2} - 2 = 0

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x^{4} + 3 x^{3} + x^{2} + 7 x - 2 = 0

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x^{4} - 3 x^{3} + 8 x^{2} + 4 = 0

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10 x^{4} - 13 x^{2} + 40 = 0

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Solution

The correct option is A $x^{4} + 3 x^{3} + 5 x^{2} - 2 = 0$
Given: equation $x^{4} - 3 x^{3} + 5 x^{2} - 2 = 0$
To find the equation whose roots are contrary to the roots of given equation
Sol: If the equation has contrary sign the only affected term will be odd degree term, as squaring the minus sign gives a positive sign term only. Hence the equation whose roots are contrary to the roots of given equation will be $x^{4} + 3 x^{3} + 5 x^{2} - 2 = 0$

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