# GMAT Prep From Platinum GMAT

### GMAT Prep Materials

### Announcement

What do you think of the new design? Send us your comments at feedback@lighthouseprep.us. Also, are there any PHP experts out there who could help fix the bug on the Practice Test page? Your help would be much appreciated!

### About Us

Platinum GMAT Prep provides the best GMAT preparation materials available anywhere, enabling individuals to master the GMAT and gain admission to any MBA program. We also provide hundreds of pages of free GMAT prep content, including practice questions, study guides, and test overviews.

If m and n are roots of the equation 2x

^{2}– 3x + 4 = 0, then what is the value of ?Correct Answer:

**A**Finding a common denominator among the terms we are looking to find and then factor the quadratic equation.

- Dividing both sides of the quadratic equation by 2 gives us the equation:

x^{2}-(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. - If we have a quadratic equation with roots m and n, it can be expressed as (x – m)(x – n) = 0. This expands to x
^{2}– (m + n)x + mn = 0. Since our equation is x^{2}- (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. - How does this help us? We want to know the value of

Finding a common denominator, we can see that:

- Thus the value we are looking for can be expressed as the sum of our roots divided by the product of our roots.
- Since we found the sum to be 3/2 and the product to be 2, we have:

- The correct answer is A.