Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationCommon RootsEasy2 minQB

MathematicsEasysingle choice

If the equations $2 x^{2} + k x - 5 = 0$ and $x^{2} - 3 x - 4 = 0$ have a common root, then the value of $k$ is

Answer:

Solution:

The roots of $x^{2} - 3 x - 4 = 0$ are $x = 4$ or $x = - 1$ .

If $x = 4$ , $2 (4)^{2} + k (4) - 5 = 0 ⟹ 32 + 4 k - 5 = 0 ⟹ 4 k = - 27 ⟹ k = - \frac{27}{4}$ .

If $x = - 1$ , $2 (- 1)^{2} + k (- 1) - 5 = 0 ⟹ 2 - k - 5 = 0 ⟹ - k = 3 ⟹ k = - 3$ .

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Common Roots

⏱ 2mℹ️ Source: QB

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