Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationLocation of rootsHard2 minPYQ_2013

MathematicsHardsingle choice

The real number $k$ for which the equation, $2 x^{3} + 3 x + k = 0$ has two distinct real roots in $[0, 1]$ belongs to

Answer:

Solution:

Given $f (x) = 2 x^{3} + 3 x + x$

$\Rightarrow f^{'} (x) = 6 x^{2} + 3$

As $f^{'} (x) > 0$ for all $x$ .

$\Rightarrow f (x)$ is a strictly increasing function for all $x$ .

Hence $f (x) = 0$ cannot have more than one root.

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Location of roots

⏱ 2mℹ️ Source: PYQ_2013

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