Final answer:
To find the value of m from the quadratic equation given the sum of the roots, we applied the sum of roots formula for a quadratic equation, arrived at the equation m² - 4 = 12, which simplifies to m² = 16. The correct value of m is 4.
Step-by-step explanation:
The student's question is asking to solve for the value of m in the quadratic equation (m²-4)x - 3x + 2 = 0, with the given sum of the roots x₁ + x₂ = 2/8. To find the value of m, we can use the sum of roots formula for a quadratic equation ax²+bx+c = 0, which states that the sum of roots x₁ + x₂ = -b/a. In our case, a = m² - 4 and b = - 3. Hence, 2/8 = -(-3)/(m² - 4).
This simplifies to 1/4 = 3/(m² - 4), and by cross-multiplying and solving for m, we find that m² - 4 = 12, m² = 16. Thus, m is either 4 or -4. However, since the coefficient of x in (m²-4) must be positive to have a sum of roots equal to 1/4, the correct answer is 4 (Option D).