Question

Decide whether $(y – 2) (y + 2) = 0$ is a quadratic equation.

Answer 1

Hint: The quadratic equation has the degree of polynomial equal to $2$. A quadratic equation should be in a form $ax^2 +bx+c =0 $ where $a \ne 0$.
The quadratic equation might or might not have a constant.

Complete step by step solution:
The equation has both left hand and right hand side and there is equality between them while polynomial is an expression of variables and constants connected by arithmetic operations. The degree of polynomial and equation is the same.
Quadratic equations have the highest power of variable equal to $2$.
The highest power of a polynomial is known as the degree of polynomial.
The equation given can be expanded to get the degree of equation:
$\begin{align}
  & (y-2)(y+2)=0 \\
 & (y\times y)+(2\times y)-(2\times y)-(2\times 2)=0 \\
 & {{y}^{2}}-4=0
\end{align}$
The power of y in LHS of above equation is $2$ while power of constant number $4$ is $0$. As $2$ is greater than $0$, the degree of the equation is $2$.
As the degree of the equation is $2$, the given equation is a quadratic equation.

Note:
> The quadratic equations are easy to solve and can be solved using various methods like the middle-term splitting method, rounding the squares method and factorization method. The commonly used method is the middle-term splitting method as it can be used to solve complex quadratic equations too in an easy manner.
> The constant term has the power of variable as zero as constant can be written in the form of constant multiply the power of variable to be equal to zero.
> The variable with power zero is equal to $1$ as per rules of variables.