Concept explainers
To find: which statements are true
Answer to Problem 119AYU
All the given statements are true
Explanation of Solution
Given:
For the cubic polynomial
The following statements will be true.
It will have only one point cutting the y-axis and that can be obtained by putting
It will intersect the x-axis at most three points and that too when all the roots of the polynomial function are real.
It will intersect the x-axis at least once; this will have at least one real root. This is true because the imaginary roots exist in pairs and the following function can have at most 3 roots. Hence, if 2 roots are imaginary, even then one root will be real and hence, it will cut the x-axis at least once.
For very large value of
But this polynomial function will not be symmetric with respect to origin. This is because when xis replaced with
Further this function will not pass through the origin because the function consists of a constant. And
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