To solve the inequality 4x^2 - 12x + 8 > 0, we first need to find the values of x where the equation is equal to zero, known as the roots of the equation.
To find the roots of the equation, we set 4x^2 - 12x + 8 = 0 and solve for x. Factoring the quadratic equation, we get:
4x^2 - 12x + 8 = 4(x^2 - 3x + 2) = 4(x - 1)(x - 2) = 0
Setting each factor to zero:
x - 1 = 0
x = 1
x - 2 = 0
x = 2
Therefore, the roots of the equation are x = 1 and x = 2.
Next, we plot these roots on a number line:
---o---1---o---2---o---
Since the inequality is greater than zero, we are looking for the values of x where the inequality is greater than zero, which is between the roots of the equation.
Therefore, the solution to 4x^2 - 12x + 8 > 0 is x ∈ (1, 2).
4x^2-12x+8> 0
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