SOLUTION: Without solving, find the product and the sum of the roots for 4x^2-7x+3 I know that a=4 b=-7 & c=3, I also have the equation, x^2+(-7)/4x +3/4 but I have no idea where to go fr

Question 707166: Without solving, find the product and the sum of the roots for 4x^2-7x+3
I know that a=4 b=-7 & c=3, I also have the equation, x^2+(-7)/4x +3/4 but I have no idea where to go from there, So where do I go from there?

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
You have the right values for a, b and c and that is all you need. You do not need to change the expression.

The sum of the roots of a quadratic is -b/a. So the sum of the roots for your expression will be -(-7)/(4) which simplifies to: 7/4

The product of the roots of a quadratic will be c/a. So the product of the roots to your expression will be (3)/(4) = 3/4

If you didn't know that the sum was -b/2a and/or that the product was c/a then it is not terribly difficult to figure this out on your own. From the Quadratic Formula we know that the roots of a general quadratic equation will be:
and
Splitting these into two separate fractions will help with the rest:
and

Now let's see what the sum looks like. If you look at and it should be easy to see that the second fractions will cancel each other out because one is positive and the other is negative. So when we add will will get:

Now let's see what the product looks like:
. If we look at this we should be able to see that this fits the pattern. And from the pattern we know that the result is . Using this pattern will save us time in multiplying:

which simplifies as follows:

These have the same denominator so we can subtract them:

Simplifying...

(Note: I have a terrible memory. I can never remember these sum and product formulas. I always go through the above to figure them out when I need them (like now)).
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