Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Let $f (x) = x^{4} + a x^{3} + b x^{2} + a x + 1$ be a polynomial where $a$ and $b$ are real numbers.

If $f (x) = 0$ has two different negative roots and two equal positive roots, then the least integral value of $a$ is

Answer:

Solution:

The two equal + ve roots must be 1,1 , and let the - ve roots be $α, \frac{1}{α} (α \neq = 1)$

Now $- a = 2 + α + \frac{1}{α} \Rightarrow a = - α - \frac{1}{α} - 2 > 0$

∴ The least integral value is ' 1 '

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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