Long-answer type questions (L.A.)
If two root of the quadratic equation `ax^(2)+7x+b=0" be "(2)/(3)and-3`, then find the value of a and b.

Explanation

`:'(2)/(3)` is a root of the equation `ax^(2)+7x+b=0`,
we get, `axx((2)/(3))^(2)+7xx(2)/(3)+b=0`
or, `(4a)/(9)+(14)/(3)+b=0`
or, `4a+42+9b=0..........(1)`
Again, since (-3) is a root of the equation `ax^(2)+7x+b=0`, we get, `axx(-3)^(2)+7xx(-3)+b=0or,9a-21+ b=0or,81a-189+9b=0,.........(2)`
Now, subracting (1) from (2) we get, 77a-231=0
or, `77a=231or,a=(231)/(77)or,a=3`.
Now putting a=3 in (1) we get, `4xx3+42+9b=0or,12+42+9b=0or,9b+54=0or,b=-(54)/(9)or,b=-6`.
`:.` The required value of a and b are a =3, b=-6.