Which of the following is a cubic polynomial?

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) polynomial is defined as an expression consisting of variables and coefficients,where the exponents of the variables must be non-negative integers

Vedclass · Accepted Answer

$p(x) = 2 - 3x - x^3$

Vedclass · Answer

(B) polynomial is defined as an expression consisting of variables and coefficients,where the exponents of the variables must be non-negative integers.$A$ cubic polynomial is a polynomial of degree $3$,meaning the highest power of the variable $x$ is $3$.In option $A$,the term $\sqrt{x}$ is $x^{1/2}$,which is not an integer.In option $B$,$p(x) = 2 - 3x - x^3$. The highest power of $x$ is $3$,and all exponents are non-negative integers. Thus,it is a cubic polynomial.In option $C$,$\sqrt{x^3} = x^{3/2}$,which is not an integer.In option $D$,the exponent $1/3$ is not an integer.Therefore,the correct option is $B$.

Similar Questions

Given that two of the zeroes of the cubic polynomial $ax^3 + bx^2 + cx + d$ are $0$, the third zero is

$A$ cubic polynomial $p(x) = 4x^3 - x$ has ...... zeros.

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0)$ are $\alpha, \beta,$ and $\gamma,$ then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} = \dots$

Verify that the numbers given alongside the cubic polynomials below are their zeroes. Also,verify the relationship between the zeroes and the coefficients in each case: $x^{3}-4x^{2}+5x-2; 2, 1, 1$.

If $1$ and $3$ are the zeros of the polynomial $p(x) = 2x^4 - 7x^3 - 13x^2 + 63x - 45$,then find the remaining zeros of $p(x)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module