Quadratic Equation and Quadratic Expression

Quadratic equations and quadratic expressions are some of the basic quadratic terminologies. These are correlated to each other. These may seem to be similar, but they have a little difference. A quadratic expression is itself an expression (ax2+bx+c), and a quadratic equation may be represented in standard form ax2+bx+c=0. Therefore, quadratic expression and equation are interrelated to each other. 

The general description of both quadratic equation and quadratic expression needs to be known before finding out the difference between these two.

What is a Quadratic Equation?

The general form of a quadratic polynomial is ax2+bx+c, where the constant a is not equal to zero. Here, the degree of the quadratic polynomial is 2.

An equation always has two sides, one on each side of the equal sign(=). When this general form of a quadratic polynomial is put equivalent to zero, the quadratic equation in standard form is obtained (ax2+bx+c =0); remember that a is not equal to zero and the constants a,b, and c are real numbers. 

The definition of a quadratic equation states that “The polynomial equation having the highest degree of two in a variable is known as a quadratic equation.”

Example of Quadratic Equation

For instance, 2x2+4x+2=0 is a quadratic equation.

Comparing it to the standard form, we get a=2, b=4, and c=2, where a is the coefficient of x2, b is the coefficient of x, and c is the constant. 

This is an example of a quadratic equation in variable x. 

-3x2 +12=0 is also a quadratic equation where x might not have power 1 in this equation, but it still is a quadratic equation because the degree of the polynomial on the left is still 2.

(Notice that in this second case, the value of the coefficient of x is zero, and that’s not a problem at all.)

The important condition is that a must not be equal to zero. Hence, we can say that a quadratic equation is of the form p of x equals zero, where p of x is a polynomial of degree two.

Quadratic Expression

Quadratic means the highest power of the variable that appears equals 2. Any expression with the highest power of the variable that appears to be equal to 2 is quadratic. An expression can not be defined in simple mathematical terms.

 x2 +5x+6 is an example of a quadratic expression. It can not be defined further in simple terms. Neither can be solved for a variable.

The number in front of the x2 is called the leading coefficient.

6x2+11x+4 is another type of quadratic expression where 6 is the leading coefficient.

These are examples of quadratic expressions in one variable.

The values of a,b and c can be found using the same approach as the quadratic equation. The value of a will be the coefficient of x2, and similarly, b and c can be found.

Quadratic Equation and Expression: Difference

A quadratic expression is a quadratic polynomial, for example, x2+6x+5, where a(coefficient of x2) cannot be equal to zero.

If a quadratic expression is equivalent to zero, then it becomes a quadratic equation like x2+6x+5=0. As the name implies, a quadratic expression contains only a quadratic term (like x2 or y2). In contrast, a quadratic equation contains a quadratic expression that is equal to any other expression(that may be quadratic or not).

Consider an example of a quadratic equation, x2+4x+3=5. Here, x2+4x+3 is a quadratic expression, and 5 is another expression. 

Conclusion

Therefore, it can be said that a quadratic equation is a mixture of different expressions containing at least one quadratic expression. 3x=12x2 is a quadratic equation made up of two expressions, where 12x2 is quadratic.

Also, a quadratic expression is something that can not be solved or factored in. An expression can not be solved to find out the variable’s value. In contrast, a quadratic equation aims to solve and determine a value that could be associated with the variable. 

These two terms are very similar, but a slight difference makes quadratic equations different.