If -5 and -7 be two roots of the equation `ax^(2)+bx+35=0`, then find the values of a and b.

Explanation

`ax^(2)+bx+35=0`
or, `a.(-5)^(2)+b.(-5)+35=0[:'(-5)` is a root ]
or, `25a-5b+35=0`
or, `5a-b+7=0...............(1)`
Also, `ax^(2)+bx+35=0`
or, `axx(-7)^(2)+bxx(-7)+35=0[:'(-7)` is a root]
or, 49a-7b+35=0
or, 7a-b+5=0…..............(2)
Now, subtracting (1) from (2), we get 2a-2=0or,2a=2or,a=1.
Putting a=1 in (1) we get, `5xx1-b+7=0`
`implies5-b+7=0implies12-b=0implies12`.
Hence a=1 and b=12.