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If tan alpha. tan beta=a and alpha +beta...

If `tan alpha. tan beta=a` and `alpha +beta =pi/3` then `tan alpha` and `tan beta` are the roots of the equation

Text Solution

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`tanalpha+tanbeta=(tanalpha+tanalpha)/(1-tanalphatanbeta)*(1-tanalphatanbeta)`
`=tan(alpha+beta)(1-tanalphatanbeta)`
`=tan(pi/6)(1-a)`
`=1/sqrt3(1-a)=(1-a)/sqrt3`
Sum of the roots is` (1-a)/sqrt3`
Product of the roots is a
`x^2-(1-a)/sqrt3x+a=0`
`sqrt3x^2-(1-a)x+sqrt3a=0`
...
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