Which values are possible rational roots of 4x3+9x2−x+10=0 according to the rational root theorem? Select each correct answer. ±
1 answer:
ANSWER
The possible rational roots are:
EXPLANATION
According to the rational root theorem, the possible rational roots of the polynomial,
are all the possible factors of the constant term divided by all the possible factors of the coefficient of the highest degree of the polynomial.
Therefore we examine the numerator and denominator of the options provided to see if they are factors of 10 and 4 respectively.
For
, we can see that 1 is a factor of 10 and 2 is a factor of 4, hence it is a possible rational root.
The same thing applies to also.
As for
, 2 is a factor of 10 but 5 is not a factor of 2, hence it is not a possible rational root.
You might be interested in
The Function having highest Degree of Four given here is :
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
1. Increasing Function.
2. Decreasing Function.
Option (4) is true .
