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If the difference of the roots of equati...

If the difference of the roots of equation `x^2 + 2px + q = 0` and `x^2 + 2qx + p =0` are equal than prove that p+q+1 = 0.(`p!=q`)

Text Solution

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`x=(-b+sqrt(b^2-4ac))/(2a)`
`=(-b-sqrt(b^2-4ac))/(2a)`
Difference`=(2sqrt(b^2-4ac))/(2a)`
`=sqrt(b^2-4ac)/a`
`sqrt(4p^2-4q)=sqrt(4q^2-4p)`
`4(p^2-q)=4(q^2-p)`
`p^2-q^2+p-q=0`
`(p-q)(p+q)+(p-q)=0`
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