# For which values of m does the equation m*x^2 – 2mx + 3 = 0 have two solution?

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justaguide | Certified Educator

Any quadratic equation ax^2 + bx + c = 0 has two different solutions if `b^2 - 4ac != 0`

For the equation m*x^2 – 2mx + 3 = 0

`(2m)^2 - 4*m*3 != 0`

=> `4m^2 - 12m != 0`

=> `4m(m - 3) != 0`

=> `m != 0 and m != 3`

**For all values of m other than 0 and 3, the equation m*x^2 – 2mx + 3 = 0 has two different solutions.**