JEE MainMathematicsEasyTheory of Equations

If a, b, p, q are non-zero real numbers, then two equations
2a^2 x^2 - 2 ab x + b^2 = 0 and p^2 x^2 + 2 pq x + q^2 = 0 have

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For equation

2a^{2}x^{2} - abx + b^{2} = 0

D_{1} = - 4a^{2}b^{2} < 0

Roots are imaginary
for equation

p^{2}x^{2} + 2pqx + q^{2} = 0

D_{2} = 0 \Rightarrow

Roots are real and equal
Hence no common roots

Source: Grass-G / M-06 Mathematics Paper 14 October.docx

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