Question

2 Points

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

O

A. Three or one

B. Two

C. One

D. Two or zero

Answer 1

Two or zero expresses the possible number of positive real solutions for the given polynomial equation.

Answer: Option D

Explanation:

Given equation:

`x^(3)-4 x^(2)-7 x+28=0`

First, we put hit and trial method to find out the one solution. So, if we put x=4 then the above expression will become zero. We can also write the above expression as

`(x-4) *\left(x^(2)-7\right)=0`

We know the formula,
`a^(2)-b^(2)=(a+b)(a-b)`, make use of this, we get

`(x-4) *(x-√(7)) *(x+√(7))=0`

So,
`x=4, √(7),-√(7)`

Hence, from the above expression, we have three values of x as x= 4, 2.64 and -2.64