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

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.