1.

If the equation `(1+m^2)x^2+2m c x+(c^2-a^2)=0`has equal roots, prove that `c^2=a^2(1+m^2)dot`

Answer» We have,
`(1+m^(2))x^(2)+2mcx+(c^(2)-a^(2))=0`
It has equal roots, if D=0
`impliesB^(2)-4AC=0`
`implies(2mc)^(2)-4(1+m^(2))(c^(2)-a^(2))=0`
`implies4m^(2)c^(2)-4(c^(2)-a^(2)+m^(2)c^(2)-m^(2)a^(2))=0`
`impliesm^(2)c^(2)-c^(2)+a^(2)-m^(2)c^(2)+m^(2)a^(2)=0`
`impliesc^(2)=a^(2)+m^(2)a^(2)=a^(2)(1+m^(2))`


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