Consider the quadratic equation 3x^2-6+2x. (a)What is the value of the discriminant? (b)What does the discriminant of the quadratic equation tell about the solutions to 3x^2-6+2x ? Thank you!

a) Since we have a quadratic equation the discriminant is given by:

Where and replacing we got:

b) Since the discriminant is higher than 0 we will have two real solutions when we set up the equation equal to 0.

Step-by-step explanation:

We have the following ufnction given:

Part a

Since we have a quadratic equation the discriminant is given by:

Where and replacing we got:

Part b

Since the discriminant is higher than 0 we will have two real solutions when we set up the equation equal to 0.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

answer: approximately 206 bones

i hope this u out a branlist and a would be greatly appreciated :