The sum of the roots of the equation 1/2x^2 - 5/4x - 3 =0 is: 5/2 2 1/2

This equation has to factor somehow or else you used the quadratic formula.

Let's start with the given equation

1/2 x^2 - 5/4 x - 3 = 0    Multiply the entire equation by 2

2* (1/2x^2 - 5/4 x - 3 = 0)  Remove the brackets. The idea is to get rid of the 1/2

2 * 5/4 = 5/2

2*1/2 x^2 - 2(5/4)x - 2*3 = 2*0    Do the multiplication

x^2 - 5/2x - 6 = 0  

Now the answer is immediate if you know how to do it. The sum of the roots is - (the middle term's coefficient) which is - (-5/2) which is + 5/2

So the answer is 5/2. That should be the sum of the roots. But we'll carry on just to show that it is right.

The equation factors, not easily, but it does factor.

(x - 4)(x + 1.5) = 0 is the way it factors. You should show this is true.

x^2 + 1.5x - 4x - 6 = 0

x^2 - 5/2 x - 6 = 0 But wait. I did say that the sum of the roots = 5/2. Where did the minus come from?

The answer to that is that we have not yet found the roots. We found the factors.

x1: (x - 4) = 0;    x = 4;    

x2:(x + 1.5) = 0;     x = - 1.5

The sum of the roots = x1 + x2 = 4 - 1.5 = 2.5 which is 5/2

So the sum of the roots = 5/2

why can't you?

step-by-step explanation:

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol