Given $P (x) = x^{4} + a x^{3} + c x + d$ such that $x = 0$ is the only real root of \displaystyle{P}'{\left({x}\right)}\text{}=\text{}{0}.\text{}{I}{f}\text{}{P}

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Given

P (x) = x^{4} + a x^{3} + c x + d

such that

x = 0

is the only real root of \displaystyle{P}'{\left({x}\right)}\text{}=\text{}{0}.\text{}{I}{f}\text{}{P}

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Question Text

Given

P (x) = x^{4} + a x^{3} + c x + d

such that

x = 0

is the only real root of \displaystyle{P}'{\left({x}\right)}\text{}=\text{}{0}.\text{}{I}{f}\text{}{P}

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