p,q,r and $s$ are integers. If the A.M. of the roots of $x^{2} - p x + q^{2} = 0$ and G.M. of the roots of $x^{2} - r x + s^{2} = 0$ are equal, then

q

is an odd integer

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r

is an even integer

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p

is an even integer

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s

is an odd integer

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Solution

The correct option is A $p$ is an even integer
$A . M = \frac{α_{1} + α_{2}}{2} = \frac{p}{2} = \sqrt{γ δ} = \sqrt{s^{2}} = G . M$
$\frac{p}{2} = s \Rightarrow p = 2 s$
As s is an integer , p is an even integer.

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p,q,r and s are integers. If the A.M. of the roots of x2−px+q2=0 and G.M. of the roots of x2−rx+s2=0 are equal, then

The correct option is A p is an even integerA.M=α1+α22=p2=√γδ=√s2=G.Mp2=s⇒p=2sAs s is an integer , p is an even integer.

p,q,r and $s$ are integers. If the A.M. of the roots of $x^{2} - p x + q^{2} = 0$ and G.M. of the roots of $x^{2} - r x + s^{2} = 0$ are equal, then

The correct option is A $p$ is an even integer
$A . M = \frac{α_{1} + α_{2}}{2} = \frac{p}{2} = \sqrt{γ δ} = \sqrt{s^{2}} = G . M$
$\frac{p}{2} = s \Rightarrow p = 2 s$
As s is an integer , p is an even integer.