Answer
Verified
419.1k+ views
Hint- Here, we will proceed by defining the quadratic polynomial and then writing down the general form of any quadratic polynomial in three variables (x, y and z), in two variables (x and y) and in one variable (x).
Complete step-by-step answer:
A quadratic polynomial is a polynomial of degree 2 or simply we can say that a quadratic polynomial is a polynomial function with one or more variables in which the highest degree term is of the second degree.
The general form of any quadratic polynomial in three variables i.e., x, y and z is given as under
$f\left( {x,y,z} \right) = a{x^2} + b{y^2} + c{z^2} + dxy + eyz + fxz + gx + hy + iz + j$ where a, b, c, d, e, f, g, h, i, j are all constants.
The general form of any quadratic polynomial in two variables i.e., x and y is given as under
$f\left( {x,y} \right) = a{x^2} + b{y^2} + cxy + dx + ey + f$ where a, b, c, d, e, f are all constants.
The general form of any quadratic polynomial in one variable i.e., x is given as under
$f\left( x \right) = a{x^2} + bx + c$ where a, b, c are all constants.
When these polynomials are equated with zero, then that equation is termed as a quadratic equation.
The general form of any quadratic equation in three variables i.e., x, y and z is given as under
$f\left( {x,y,z} \right) = a{x^2} + b{y^2} + c{z^2} + dxy + eyz + fxz + gx + hy + iz + j = 0$ where a, b, c, d, e, f, g, h, i, j are all constants.
The general form of any quadratic equation in two variables i.e., x and y is given as under
$f\left( {x,y} \right) = a{x^2} + b{y^2} + cxy + dx + ey + f = 0$ where a, b, c, d, e, f are all constants.
The general form of any quadratic equation in one variable i.e., x is given as under
$f\left( x \right) = a{x^2} + bx + c = 0$ where a, b, c are all constants.
Note- In this particular problem, out of all the quadratic polynomials the general form of quadratic polynomial in one variable is usually used. The solution of the quadratic equation in one variable i.e., $f\left( x \right) = a{x^2} + bx + c = 0$ is either solved by factorization method or by discriminant method.
Complete step-by-step answer:
A quadratic polynomial is a polynomial of degree 2 or simply we can say that a quadratic polynomial is a polynomial function with one or more variables in which the highest degree term is of the second degree.
The general form of any quadratic polynomial in three variables i.e., x, y and z is given as under
$f\left( {x,y,z} \right) = a{x^2} + b{y^2} + c{z^2} + dxy + eyz + fxz + gx + hy + iz + j$ where a, b, c, d, e, f, g, h, i, j are all constants.
The general form of any quadratic polynomial in two variables i.e., x and y is given as under
$f\left( {x,y} \right) = a{x^2} + b{y^2} + cxy + dx + ey + f$ where a, b, c, d, e, f are all constants.
The general form of any quadratic polynomial in one variable i.e., x is given as under
$f\left( x \right) = a{x^2} + bx + c$ where a, b, c are all constants.
When these polynomials are equated with zero, then that equation is termed as a quadratic equation.
The general form of any quadratic equation in three variables i.e., x, y and z is given as under
$f\left( {x,y,z} \right) = a{x^2} + b{y^2} + c{z^2} + dxy + eyz + fxz + gx + hy + iz + j = 0$ where a, b, c, d, e, f, g, h, i, j are all constants.
The general form of any quadratic equation in two variables i.e., x and y is given as under
$f\left( {x,y} \right) = a{x^2} + b{y^2} + cxy + dx + ey + f = 0$ where a, b, c, d, e, f are all constants.
The general form of any quadratic equation in one variable i.e., x is given as under
$f\left( x \right) = a{x^2} + bx + c = 0$ where a, b, c are all constants.
Note- In this particular problem, out of all the quadratic polynomials the general form of quadratic polynomial in one variable is usually used. The solution of the quadratic equation in one variable i.e., $f\left( x \right) = a{x^2} + bx + c = 0$ is either solved by factorization method or by discriminant method.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Select the word that is correctly spelled a Twelveth class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE