Question

If x = − 3 and` x = 2/3 `are solution of quadratic equation `mx^2 + 7x + n = 0`, find the values of m and n.  

Answer 1

`mx^2 + 7x + n = 0`
Put x = − 3 in given equation
`m (−3)^2 + 7(−3) + n = 0`
⟹ 9m – 21 + n = 0
9m + n = 21 ------------ (1) 

Put x = `2/3` in given equation 

`m(2/3)^2+7(2/3)+n=0` 

⟹`(4m)/9+14/3+n=0`

⟹4m + 9n = − 42 .....................(2) 

Solving these equations we get
m = 3 and n = − 6