Assertion :I: The equation $f (x) = 4 x^{5} + 20 x - 9 = 0$ has only one real root. Reason: II: $f^{'} (x) = 20 x^{4} + 20 = 0$ has no real root.

Statement I is true,Statement II is also true; Statement II is the correct explanation of Statement I

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Statement I is true,Statement II is also true; Statement II is not the correct explanation of Statement I

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Statement I is true,Statement II is false

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Statement I is false,Statement II is true

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Solution

The correct option is A Statement I is true,Statement II is also true; Statement II is the correct explanation of Statement I
Given equation is $4 x^{5} + 20 x - 9 = 0$
Fifth degree equation must have at least one real root.
If it had two real roots, $f^{'} (x) = 0$ must have one real root.
Hence, Option A is correct.

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