The area enclosed by `f(x)=12+ax+-x^(2)` coordinates axes and the ordinates at `x=3(f(3)gt0)` is 45 sq. units. If m and n are the x-axis intercepts of the graph of y=f(x), then the value of (m+n+a) si ___.

Answer

8

Explanation

`overset(3)underset(0)int(-x^(2)+ax+12)dx=45" gives "a=4`
Hence, `f(x)=12+4x-x^(2)=(2+x)(6-x)`
Hence, `m=-2 and n=6`
`m+n+a=6-1+4=8`