Question

Which of the following is quadratic polynomial
\[{\text{A }}x + 2\]
\[{\text{B }}{x^2} + 2\]
\[{\text{C }}{x^3} + 2\]
\[{\text{D }}2x + 2\]

Answer 1

Hint: The given question is to find out that out of four polynomials, which one is a quadratic polynomial. We will check these options one by one where a quadratic polynomial is an expression that includes addition and subtraction of some higher powers of variable and constant.

Complete step-by-step answer:
 The question is to find out that out of the given \[4\] options, which one is quadratic polynomial.
Polynomial is of the type
\[{a_0}{x^n} + {a_1}{x^{n - 1}} + {a_2}{x^{n - 2}} + ...\]
Where \[{a_0},{a_1},{a_2}...\]are the constants whose value is fixed.
and x is the variable and \[n,n - 1,n - 2,...\] are the powers of the variables.
Here quadratic polynomial is the polynomial in which the maximum power of the variable is \[2\]or in other words we can say that if the maximum power of the polynomial is \[2,\] that means the polynomial is quadratic polynomial otherwise not. We will check all the options one after another .
In option \[(1),\] we have to check that \[(x - 2)\] is a quadratic polynomial or not. Since in \[(x - 2)\]\[,\] the maximum power of a variable is \[1\]\[,\] therefore this is not quadratic polynomial.
In \[(2),\]\[{x^2} - 2\] is given\[,\] here maximum power of variable is \[2,\] therefore it is a quadratic polynomial. So option \[(2)\]is correct
In \[(3),\]\[{x^3} - 2\] is given\[,\] here maximum power of variable is \[3,\] therefore it is not quadratic polynomial.
In \[(4),\]\[(2x - 2)\] is given\[,\] here maximum power of variable is \[1,\] therefore it is also not quadratic polynomial.

Note: Quadratic polynomial is of the type \[a{x^2} + bx + c\] where \[{\text{a,b and c}}\] are constants and \[x\] is variable. To solve this quadratic polynomial, we can use any of the three methods which are middle term splitting and method of discriminant and with every method \[,\] we get the same factors.