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If 4a+2b+c=0 , then the equation 3ax^(2)...

If `4a+2b+c=0` , then the equation `3ax^(2)+2bx+c=0` has at least one real lying in the interval `(0,2)`

Text Solution

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Let `f(x)=ax^3+bx^2+cx+d`` \ \ \ \ ...(i)`

`f(0)=d`

`f(2)=a(2)^3+b(2)^2+c(2)+d`

`f(2)=8a+4b+2c+d`

`f(2)=2(4a+2b+c)+d`

`f(2)=2(0)+d`

`f(2)=d`

As per Rolle's theorem,

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