Question

**PLEASE HELP ASAP**

Answer 1

The Function having highest Degree of Four given here is :

        $f(x) = x^4 - 2 x^3 - 9 x^2 + 2x + 8?$

As the given function has highest degree of four, it has maximum of four roots.

As complex and Irrational root occur in pairs, so There are many possibilities

1. Two Complex or Irrational + Two Real

2. Four real roots

3.All roots are complex or irrational

By looking at the options described below, it means it has four real roots.

It will cut X axis at four points.

With the help of Desmos you can directly find the solution of this problem, but without desmos Graphing, we first have to check by Taking different points on the curve whether graph of function described here is correct or not, i.e by method of increasing and decreasing formula of a function.The method to check is

If there are two points on the curve i.e $(x_{1},y_{1}), (x_{2},y_{2}$

1.  $If ,x_{2} > x_{1} and y_{2} >y_{1}$  Increasing Function.

2.  $If ,x_{2} > x_{1} and y_{2}$  Decreasing Function.

Option (4) is true .