If The equation ${ x }^{ 2 }+2\left( k+1 \right) x+9k-5=0$ has only negative roots, then $k\le 6$
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Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
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Assertion is correct but Reason is incorrect.
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Both Assertion is incorrect and Reason are correct.
For the equation x squared plus two times the quantity k plus one times x plus nine k minus five equals zero to have only negative roots, both the sum and the product of the roots must be negative. The sum of roots is negative two times the quantity k plus one, so k must be greater than negative one. The product of roots is nine k minus five, requiring k to be less than five ninths, which directly contradicts the claim that k can be any value up to 6. Thus, the assertion is incorrect, while the standard rule for analyzing negative roots via the sum and product is correct.