1.

Solve the following quatratic equation : a^(2)b^(2)x^(2)+b^(2)x-a^(2)x-1=0

Answer»

`(-1)/(a)and(1)/(b)`
`(-1)/(a^(2))and(1)/(b^(2))`
`(1)/(a^(2))and(1)/(b^(2))`
`(-1)/(a^(2))and(-1)/(b^(2))`

SOLUTION :Given equation is `a^(2)b^(2)X^(2)+b^(2)x-a^(2)x-1=0`
`impliesb^(2)x(x+1)-1)(a^(2)x+1)=0`
`IMPLIES(a^(2)x+1)(b^(2)x-1)=0`
`impliesa^(2)x+1=0orb^(2)x-1=0`
when `a^(2)x+1=0impliesx=-(1)/a^(2)` and `b^(2)x-1=0+impliesx=(1)/b^(2)`
HENCE, `-(1)/(a^(2))and(1)/(b^(2))` are roots of the equation.


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