Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsEasy2 minPYQ_2020

MathematicsEasysingle choice

If $α$ and $β$ are the roots of the equation $2 x (2 x + 1) = 1$ , then $β$ is equal to :

Answer:

Solution:

Given equation is

$2 x (2 x + 1) = 1 \Rightarrow 4 x^{2} + 2 x - 1 = 0$ .........(1)

roots of equation $(1)$

are $α$ and $β$

$∴ α + β = - \frac{1}{2}$

$\Rightarrow β = - \frac{1}{2} - α$ ........(2)

and

$4 α^{2} + 2 α - 1 = 0 \Rightarrow α^{2} = \frac{1}{4} - \frac{α}{2}$ .........(3)

now

$- 2 α (α + 1) = - 2 α^{2} - 2 a$

$= - 2 (\frac{1}{4} - \frac{α}{2}) - 2 α = - \frac{1}{2} - α = β$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Theory of equations

⏱ 2mℹ️ Source: PYQ_2020

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