An expression which consists of constant, variables and exponent values is known as polynomial expression. The polynomial expression is combined with the addition, subtraction, and multiplication.
Like 5x2 + 9x + 12 = 0;
This given expression is a polynomial expression and one exponent value is present in this expression.
The expression which contains a Square root values is known as radical expression.
For example: √6, 3√ x + 2, 8√ 16 and 6 + 3√ 12; these all are radical expressions.
The symbol ‘√’ is used to represents the square root or n th roots of the expression.
The other definition, an expression which contains the radical expression with the variable in the radicands is also known as radical equation.
Here we will be exploring Polynomials and radical expression.
Suppose we have a radical expression
Where the value of ‘x’ is 3 and the value of ‘y’ is 9 and we have to solve the radical expression;
For solving this expression we follow some steps:
The given expression is
And value of ‘x’ and ‘y’ is 3 and 9;
Step 1: First substitute the values of ‘x’ and ‘y’ in the given radical expression.
Step 2: Then we find the positive square root.
Step3: Then solve the expression.
Now we will see how to solve polynomial expression;
Suppose we have 3x2 -5x + 3 at x - 4;
For solving this expression we have to follow some steps:
Step 1: First we have a polynomial expression.
Step 2: Then put the value of ‘x’ as -4.
=> 3x2 -5x + 3;
On putting the value of x = -4 we get:
=> 3(-4)2 -5(-4) + 3;
Step 3: Then we solve the expression:
=> 3 * 16 + 20 + 3;
=> 48 + 23;
Quadratic equation can be defined as polynomial equation with highest degree ‘2’. Quadratic equation can also be called as a second degree equation. Consider the following function f (X) = J X2 + KX + L, Since highest degree of variable 'X' is two (2) hence it is called as Quadratic Equation. J, K and L are quadratic coefficients. Let’s see how to...Read More
Quadratic equation is an equation whose highest degree is two. Degree 2 indicates that highest power in equation is two.
Let’s discuss process of solving Quadratic Equation by factoring. Let’s consider the following quadratic equation to understand how to solve quadratic equations by factoring?
A y2 + B y + C = 0,
Since maximum degree of varia...Read More
Standard Quadratic Equation is written in form ax2 + b x + c = 0, but in case of quadratic inequalities expression is written in as,
1.) ax2 + b x +c > 0, example: x2 + 4x > 5,
2.) ax2 + b x +c < 0, example: 8x2 < 29,
3.) ax2 + b x +c < 0, example : 6 ≥ x2 – x,
4.) ax2 + b x +c <= 0, example : 4y2 + 1 ≤ 8y,
There are some steps for solving...Read More
Quadratic equation is written as ax2 + bx + c = 0, from this equation we can calculate Quadratic Formulas and Discriminant. Quadratic formula is given as: (-b ∓ √(b2 – 4ac))/2a , this formula is called, this formula gives us two solutions, x1 = (-b + √( b2 – 4ac))/2a and x2 = (-b - √(b2 – 4ac))/ 2a. Similarly we can find the Discriminant, discrimina...Read More
An equation with highest degree of 2 is called as Quadratic Equation. We can say that an equation in which highest power is a Square is known as quadratic equation. If highest power is more than 2 then it is not a quadratic equation. It can be written as: ax2 + bx + c = 0 and Quadratic Formula is given by:
⇨ x = - b + √ (b2 – 4ac) / 2a, its alt...Read More
Quadratic equation is a trinomial that means this equation has three terms. Standard form of Quadratic Equation is ax2 + bx +c. Here a, b and c are constants. Let us discuss the process of Solving Quadratic Equations by completing squares.
In mathematics completing the Square means to find the last term of perfect square trinomial. When...Read More