Question

The value of m for which the expression (2x²-5x+3)/(4x-m) can take all real values for x € R-{m/4}

Answer 1

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Answer 2

m ∈ 2, -12.

Dividing 2x²-5x+3 by 4x-m,

we get the quotient as $\frac{x}{2}$ - $\frac{m-10}{8}$ and remainder as $\frac{m*(m-10)}{8}$ - 3

For x to take all real values, 2x²-5x+3 should be completely divsible by 4x-m.

∴ Remainder must be equal to zero

∴ $\frac{m*(m-10)}{8}$ -3 = 0

∴ m² - 10m -24 = 0

∴ m² - 12m + 2m - 24 = 0

∴ m = 2 or m = -12