1.

If 0 lt alphalt beta lt gamma lt pi//2, then the equation (x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)=0 has

Answer»

real and unequal ROOTS
non-real roots
real and equal roots
real and unequal roots greater than `2`

Solution :`(a)` Let `F(x)=(x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)`
Now, `f(sin ALPHA)=(sinalpha-sinbeta)(sinalpha-singamma)`
`=(-)(-)=positive
`f(sinbeta)=(sinbeta-sinalpha)(sinbeta-sinalpha)=(+)(-)=`negative
`f(sin gamma)=(sin gamma-sinalpha)(singamma-sinbeta)=(+)(+)=`positive
`IMPLIES "Roots of " f(x)=0` are real and distinct.


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