If a, b, p, q are non zero real numbers, then how many common roots would two equation $2 a^{2} x^{2} - 2 a b x + b^{2} = 0$ and $p^{2} x^{2} + 2 p q x + q^{2} = 0$ have?

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Solution

For equation $2 a^{2} x^{2} - a b x + b^{2} = 0$
$D_{1} = 4 a^{2} b^{2} - 8 a^{2} b^{2} = - 4 a^{2} b^{2} < 0$
Therefore, roots are imaginary.
For equation $p^{2} x^{2} + 2 p q x + q^{2} = 0$ ,
$D_{2} = 4 p^{2} q^{2} - 4 p^{2} q^{2} = 0$
Therefore, roots are real and equal.
Hence, no common roots.

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Similar questions

If a,b,p,q are non-zero real numbers, then the two equations $2 a^{2} x^{2} - 2 a b x + b^{2} = 0$ and $p^{2} x^{2} + 2 p q x + q^{2} = 0$ have

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