3. Solve the following quadratic equations.

4x2 = 0
4x2-3x = 0
x2 + 5x + 6 = 0
n2-5n + 4 = 0
3x2 + x-2 = 0
6x2 + 3x-3 = 0

4. Given the following rectangle, determining obligations should be the value of x that allows to obtain the area indicated.

Part 3)

a)

b) and

c) and

d) and

e)  and

f)  and

Part  4)

Step-by-step explanation:

Part 3) Solve the following quadratic equations.

case a) we have

Divide by 4 both sides

take square root both sides

case b) we have

Factor x

so

One solution is

Second solution is

case c) we have

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

therefore

case d) we have

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

therefore

case e) we have

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

therefore

case f) we have

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

therefore

Part 4) we know that

The area of rectangle is equal to

we have

substitute

solve for x

Apply distributive property right side

solve the quadratic equation by formula

we have

substitute in the formula

therefore

 ----> the value of x cannot be negative

so

The solution is x=10 cm