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If one of the roots of x^2+(1+k)x+2k=0 i...

If one of the roots of `x^2+(1+k)x+2k=0` is twice the other, then `(a^2+b^2)/(ab)=`

Text Solution

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Let `a` and `b` are the roots of the given equation such that ` 2a = b`.
Her, product of roots ,` a*b = (2k)/1`
`=>ab = 2k`
`=>a(2a) = 2k => a^2 = k`
Then, `(a^2+b^2)/(ab) = (a^2+4a^2)/(2k)`
`= (5k)/(2k) = 5/2`
`:. (a^2+b^2)/(ab) = 5/2.`
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