Exploring Polynomials And Radical Expression

posted on: 28 May, 2012 | updated on: 21 Sep, 2012

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 $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»6«/mn»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»2«/mn»«msqrt»«mi»y«/mi»«/msqrt»«/mrow»«mi»x«/mi»«/mfrac»«/math»$
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 $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»6«/mn»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»2«/mn»«msqrt»«mi»y«/mi»«/msqrt»«/mrow»«mi»x«/mi»«/mfrac»«/math»$
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.
=> $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»6«/mn»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»2«/mn»«msqrt»«mn»9«/mn»«/msqrt»«/mrow»«mn»3«/mn»«/mfrac»«/math»$
Step 2: Then we find the positive square root.
=> $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»6«/mn»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»2«/mn»«mo»(«/mo»«mn»3«/mn»«mo»)«/mo»«/mrow»«mn»3«/mn»«/mfrac»«/math»$
Step3: Then solve the expression.
=> $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»12«/mn»«mn»3«/mn»«/mfrac»«/math»$
=> 4;
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;
=> 71;

Topics Covered in Exploring Polynomials And Radical Expression

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posted on: 20 Aug, 2012 | updated on: 21 Aug, 2012

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posted on: 21 Aug, 2012 | updated on: 21 Sep, 2012

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posted on: 21 Aug, 2012 | updated on: 22 Aug, 2012

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posted on: 22 Aug, 2012 | updated on: 23 Aug, 2012

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posted on: 22 Aug, 2012 | updated on: 23 Aug, 2012

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posted on: 24 Aug, 2012 | updated on: 25 Aug, 2012

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