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rss GMAT Practice Question (One of Hundreds)
If m and n are roots of the equation 2x2 – 3x + 4 = 0, then what is the value of Figure 1?
Correct Answer: A
Finding a common denominator among the terms we are looking to find and then factor the quadratic equation.
  1. Dividing both sides of the quadratic equation by 2 gives us the equation:
    x2 -(3/2)x + 2 = 0
    This is very difficult to factor, but we do not actually have to factor it. We can use a nice property of quadratic equations to finish the problem.
  2. If we have a quadratic equation with roots m and n, it can be expressed as (x – m)(x – n) = 0. This expands to x2 – (m + n)x + mn = 0. Since our equation is x2 - (3/2)x + 2 = 0, we know the sum of its roots, m + n, is 3/2 and the product of its roots, mn, is 2.
  3. How does this help us? We want to know the value of Figure 1
    Finding a common denominator, we can see that:
    Figure 2
  4. Thus the value we are looking for can be expressed as the sum of our roots divided by the product of our roots.
  5. Since we found the sum to be 3/2 and the product to be 2, we have:
    Figure 3
  6. The correct answer is A.