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If 2a+3b+6c = 0, then show that the equa...

If 2a+3b+6c = 0, then show that the equation `a x^2 + bx + c = 0` has atleast one real root between 0 to 1.

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`"Let "f(x) =(ax^(2))/(3)+(bx^(2))/(2)+cx`
`f(0) =0 " " and" "f(1) =(a)/(3)+(b)/(2) +c =2a +3b +6c =0`
`"if "" " f(0) =f(1) " then " f(x) =0 " for some value of " x in (0,1)`
`rArr " "ax^(2) +bx +c =0` for at least one `x in (0,1)`
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