Question

Find the value of m and n for which x= 2 and x=3 are solution of the equation
3x^2 - 2mx + 2n= 0​

Answer 1

The question above is when -2n not +2n. The answer of the above is not correct.

Solution: Compare the coefficients.

Two solutions are x=2 or x=3.

This tells us the form of the equation is in k * (x² - 5x + 6) = 0,

but this equation should become 3x² - 2mx + 2n = 0​.

By comparing both numbers, we get k=3.

3 * (x² - 5x + 6) = 0 is 3x² - 2mx + 2n = 0 itself.

It is required that 3x² - 15x + 18 = 3x² - 2mx + 2n.

By comparing x: -15x = -2mx → 2m = 15 → ∴ m = 15/2

By comparing numbers: 18 = 2n → ∴ n = 9

Therefore, the solutions are m = -15/2 and n = 9.

Answer 2

Find the value of m and n for which x= 2 and x=3 are solution of the equation

3x^2 - 2mx + 2n= 0​