Without his pencil or calculator, joey knows that 2x³+3x²− 1 = 0 has at least one real solution. how does he know?

Find the discriminant

Check explanation

Step-by-step explanation:

b^2-4ac

if it is equal to 0 there is no solution

Greater then 0 there is 2 real solution

Less then 0 there is 1 real

3^2-4(2*-1)

9-4(-2)

9(8)

72 there is at least one real solution

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²