Question bank/JEE Main/Mathematics
JEE MainMathematicsModerateQuadratic Equations
x^2 + ax + 1 = 0 x^2 - x - a = 0
a
Show answer and solution
Let α be a real common root. Then
α^2 + aα - a = 0
α^2 - α - a = 0
Therefore,
α (a + 1) + (a + 1) = 0
(a + 1) (α + 1) = 0
If a = - 1, then the equations are same and also cannot have a real
root. therefore a+ 1 ≠0 and hence α= - 1, so that a = 2
α^2 + aα - a = 0
α^2 - α - a = 0
Therefore,
α (a + 1) + (a + 1) = 0
(a + 1) (α + 1) = 0
If a = - 1, then the equations are same and also cannot have a real
root. therefore a+ 1 ≠0 and hence α= - 1, so that a = 2
Source: Grass-G / M-03 Paper 1 Mathematics 21-8-2020_Final.docx
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