If `x^2+2a x+a<0AAx in [1,2],` the find the values of `adot`

Explanation

Given ,
`x^(2) + 2ax + a lt 0. AA x in` [1, 2]
Hence, 1 and 2 lie between the roots of the equation
` x^(2) + 2ax + a = 0`
`rArr f(1) lt 0 and f(2) lt 0`
`rArr 1 + 2a + a lt 0, 4 + 4a + a lt 0`
`rArr a lt -(1) /(3) , a lt -(4)/(5)`
`rArr a in ( - infty, - (4)/(5))`