TopThe expressions or equations which consist of variables and constants with some operators like +, -, /, * are called algebraic expressions. These expressions are in various forms according to the degree of polynomial. Polynomial is generally those expressions which consist of variables and constants with non-negative degree. Quadratic polynomial has a degree of two because the highest degree of variable is 2. Equation of quadratic polynomial is of the form,
ax2 + bx + c,
Where ‘x’ is a variable and a, b, c are respectively constant real Numbers where ‘a’ should not be zero. Here we can easily see that the highest degree of ‘x’ is 2 which satisfy the condition of quadratic polynomial. Let's take another example of quadratic polynomial where the values of a, b and c are respectively 3, 5, 8 so the equation of Quadratic Equation after putting these values in above equation.
a=3, b=5 and c=8,
3*x2 + 5*x + 8,
3x2 + 5x + 8,
Now the final result is as a quadratic polynomial which contains a degree of 2. Here the highest degree of ‘x’ is 2 which satisfy the quadratic polynomial property. And all the values of constant are Real Numbers which is also true for that equation. Quadratic polynomial can also contain more than one variable with it. So if the quadratic polynomial which contains more than one variable must have to satisfy the condition in which any one should have a highest degree of 2. In that case general form of the equation is
ax2 + bxy + cy2 + dx + ey + f,
In this case we can easily see that variable ‘a’ and ‘b’ consists of degree of 2 which satisfy the condition of quadratic polynomial having two variables. Now let's take an example:-
5x2 + 3xy + 2y2 + 4x + 7y + 1,
In that example we can clearly see that both variables ‘x’ and ‘y’ contain highest degree of 2. Where the values of a, b, c, d and e are respectively 5, 3, 2, 4, 7 and 1. So we can say that a quadratic polynomial has a degree of 2.