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

No common root

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Two common roots if $3 p q = 2 a b$

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One common root if $2 a^{2} + b^{2} = p^{2} + q^{2}$

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Two common roots if $3 b q = 2 a p$

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Solution

The correct option is A
No common root

$2 a^{2} x^{2} - 2 a b x + b^{2} = 0$
$Δ_{1} = 4 a^{2} b^{2} - 8 a^{2} b^{2}$
$\Rightarrow Δ_{1} < 0$

$p^{2} x^{2} + 2 p q x + q^{2} = 0 Δ_{2} = 4 p^{2} q^{2} = 4 p^{2} q^{2} = 0 \Rightarrow Δ_{2} = 0$

$∴$ No common root

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Similar questions

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

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

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

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

a, b, c, p, q, r

\frac{p}{a} + \frac{q}{b} + \frac{r}{c} = 1 + i

\frac{a}{p} + \frac{b}{q} + \frac{c}{r} = 0,

\frac{p^{2}}{a^{2}} + \frac{q^{2}}{b^{2}} + \frac{r^{2}}{c^{2}}

a, b, c, p, q, r

\frac{p}{a} + \frac{q}{b} + \frac{r}{c} = 1 + i

\frac{a}{p} + \frac{b}{q} + \frac{c}{r} = 0

\frac{p^{2}}{a^{2}} + \frac{q^{2}}{b^{2}} + \frac{r^{2}}{c^{2}}

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