Question

Which of the following is a quadratic polynomial?
A. \[p(x) = 5{x^0} + 10\]
B. \[p(x) = 5{x^1} + 10\]
C. \[p(x) = 5{x^3} + 10\]
D. \[p(x) = 5{x^2} + 10\]

Answer 1

Hint: Lets check the option using the condition of a polynomial to be a quadratic polynomial, which is, quadratic polynomials are the type of polynomial whose leading coefficients have degree 2 and the value of leading coefficient should not be zero. So, we have to check option one by one and whenever we find the polynomial satisfying above condition that will be our required answer.

Complete step by step answer:

As given that we have to select quadratic polynomial
So, consider the polynomial whose leading coefficient is not zero and should be of degree two.
Hence, checking option individually
\[p(x) = 5{x^0} + 10\], this polynomial is of degree zero.
\[p(x) = 5{x^1} + 10\], this polynomial has degree as one.
\[p(x) = 5{x^3} + 10\], being polynomial of degree three it is cubic polynomial.
\[p(x) = 5{x^2} + 10\], here the polynomial has degree two and also the leading coefficient is not zero.
Hence, it is the required quadratic polynomial.
Hence, option (D) is correct answer.

Note: In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is \[{x^2} - 4x + 7.\]. In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree.