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Standard XII

Mathematics

Common Roots

p, q, r, and ...

Question

$p, q, r,$ and $s$ are integers. If the $A M$ of the roots of the quadratic equation $x^{2} - p x + q^{2} = 0$ and $G M$ of the roots of the quadratic equation $x^{2} - r x + s^{2} = 0$ 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 C $p$ is an even integer
A.M of the roots of $x^{2} - p x + q^{2} = 0$ is $= 1 / 2$ (sum of roots) $= p / 2$
and G.M of the roots of $x^{2} - r x + s^{2} = 0$ is $=$ (sum of roots $)^{2} = s$
According to given condition $p = 2 s$
and given $p, q, r, s$ are integer therefore p must be even integer

Suggest Corrections

Similar questions

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p,q,r, and s are integers. If the AM of the roots of the quadratic equation x2−px+q2=0 and GM of the roots of the quadratic equation x2−rx+s2=0 are equal then

The correct option is C p is an even integerA.M of the roots of x2−px+q2=0 is =1/2(sum of roots)=p/2and G.M of the roots of x2−rx+s2=0 is = (sum of roots)2=sAccording to given condition p=2sand given p,q,r,s are integer therefore p must be even integer

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