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 all the roots are imaginary and $b = - 1$ then number of all possible integral values of $a$ is

Answer:

Solution:

Given equation is $t^{2} + at - 3 = 0$ where $t = x + \frac{1}{x}$ both roots must lie between $- 2, 2$ $\Rightarrow \frac{- 1}{2} < a < \frac{1}{2}$

$\Rightarrow a = 0$

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

⏱ 2mℹ️ Source: QB

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