The area enclosed by `f(x)=12+a x+-x^2` coordinates axes and the ordinates at `x=3(f(3)>0)` is 45 sq. units. If `ma n dn` are the x-axis intercepts of the graph of `y=f(x),` then the value of `(m+n+a)` is____

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`