State the possible number of positive real zeros, negative realzeros, and imaginary zeros for each function.
13.f(x) = ­-x^3 -­ x2 + 14x -­ 24

14.f(x) = 2x^3 -­ x^2 + 16x -­ 5

In general, y = ax³ + bx² + cx + d

Where a,b,c & d are real,

Y can have at max 3 real roots, or one real and a conjugate pair of complex roots.

Also, -d/a is the product of roots

13) positive real values: 0 or 2

negative real values: 1 or 3

Imaginary roots: 0 or 2

14) positive real values: 1 or 3

negative real values: 0 or 2

Imaginary roots: 0 or 2

A rectangle is a parallelogram with at least one right angle is the best choice ⇒ answer A

Step-by-step explanation:

* Lets revise the properties of the rectangle

# Each two opposite sides are parallel

# Each two opposite sides are equal in length

# Its two diagonals bisect each other  and equal each other

# Its four angles are right angles

- The parallelogram can be a rectangle if:

# Two adjacent sides are perpendicular to each other means one

  angle of its four angles is a right angle

- OR

# Its two diagonals are equal in length

* Lets solve the problem

- We will study the answers to chose the best one

# Answer A

- A rectangle is a parallelogram with at least one right angle

∵ Each tow opposite angles are equal in the rectangle

∵ One of the is right angle means its measure is 90°

∴ The measure of the opposite angle is also 90°

∵ The sum of the measures of the four angles is 360°

∴ The sum of the measures of the other two angles is;

   360 - (90 + 90) = 180°

∵ They are equal to each other (opposite angles)

∴ The measure of each one = 180 ÷ 2 = 90°

∴ The measure of the four angles are 90°

∴ The four angles of the rectangle are right angles

* A rectangle is a parallelogram with at least one right angle is the

 best choice