Question

If x = -3 and x = 2/3 are solutions of quadratic equation mx² + 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 equation we get

m = 3 and n = -6