Question

Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?

x^3-4x^2-7x+28=0

A. Three or one
B. One
C. Two
D. Two or zero

(Thank you for the help, by the way. Please explain the answer, I'm not good at this D:)

Answer 1

there are 2 changes of sign so it has 2 or zero positive roots.

Answer 2

Answer: The answer is (D). Two or zero.

Step-by-step explanation: The given polynomial equation is

$x^3-4x^2-7x+28=0.$

We are to select the correct option that will express the positive real solutions for the above polynomial equation.

Since the given equation is cubic, there must be at least one real root. Also, if the second root of the equation comes out to be real, then the third one must also be real.

If all the roots are positive and real, then the constant term must involve negative sign.

If there is no positive real root, then the constant term will be positive.

If there is one positive real root, then the constant term will be negative.

If there is two positive real roots, then the constant term will be positive.

Hence, there can be two or zero positive real roots.

Thus, the correct option is (D).