## FINDING SQUARE ROOT OF A POLYNOMIAL

Finding Square Root of a Polynomial :

In this section, you will learn how to find square root of a polynomial using long division.

Before look at the stuff finding square root of a polynomial, you are advised to look at the stuff finding square root of a number using long division step by step.

To have the stuff on finding square root of a number using long division,

Note :

Before proceeding to find the square root of a polynomial, one has to ensure that the degrees of the variables are in descending or ascending order.

## Finding Square Root of a Polynomial - Examples

Example 1 :

Find the square root of the following polynomial :

x4 - 4x3 + 10x2 - 12x + 9

Solution : Therefore the square root of the given polynomial is

|x2 - 2x + 3|

Example 2 :

Find the square root of the following polynomial :

4x4 + 8x3 + 8x2 + 4x + 1

Solution : Therefore the square root of the given polynomial is

|2x2 + 2x + 1|

Example 3 :

Find the square root of the following polynomial :

9x4 - 6x3 + 7x2 - 2x + 1

Solution : Therefore the square root of the given polynomial is

|3x2 - x + 1|

Example 4 :

Find the square root of the following polynomial :

4 + 25x2 - 12x - 24x3 + 16x4

Solution :

First arrange the term of the polynomial from highest exponent to lowest exponent and find the square root.

Then,

16x4 - 24x3 + 25x2 - 12x + 4 Therefore the square root of the given polynomial is

|4x2 - 3x + 2|

Example 5 :

Find the values of a and b if the following polynomial is a perfect square

4x4 - 12x3 + 37x2 + ax + b

Solution : Because the given polynomial is a perfect square,

a + 42  =  0  and  b - 49  =  0

Solving the above equations for a and b, we get

a  =  -42

b  =  49

Example 6 :

Find the values of a and b if the following polynomial is a perfect square

x4 - 4x3 + 10x2 - ax + b

Solution : Because the given polynomial is a perfect square,

-a + 12  =  0  and  b - 9  =  0

Solving the above equations for a and b, we get

a  =  12

b  =  9

Example 7 :

Find the values of a and b if the following polynomial is a perfect square

ax4 + bx3 + 109x2 - 60x + 36

Solution :

Here a and b are being the coefficients of x4 and x3 respectively.

To solve for a and b, always they have to come at last.

So, write the given polynomial from lowest exponent to highest exponent.

36 - 60x + 109x2 + bx3 + ax4 Because the given polynomial is a perfect square,

bx3 + 70x3  =  0  and  ax4 - 49x4  =  0

Solve the above equations for a and b.

 bx3 + 70x3  =  0(b + 70)x3  =  0Divide each side by x3.b + 70  =  0b  =  -70 ax4 - 49x4  =  0(a - 49)x4  =  0Divide each side by x4.a - 49  =  0 a  =  49

Therefore,

a  =  49

b  =  -70

Example 8 :

Find the values of a and b if the following polynomial is a perfect square

ax4 - bx3 + 40x2 + 24x + 36

Solution :

Here a and b are being the coefficients of x4 and x3 respectively.

To solve for a and b, always they have to come at last.

So, write the given polynomial from lowest exponent to highest exponent.

36 + 24x + 40x2 - bx3 + ax4 Because the given polynomial is a perfect square,

-bx3 - 12x3  =  0  and  ax4 - 9x4  =  0

Solve the above equations for a and b.

 -bx3 - 12x3  =  0(b + 12)(-x3)  =  0Divide each side by (-x3).b + 12  =  0b  =  -12 ax4 - 9x4  =  0(a - 9)x4  =  0Divide each side by x4.a - 9  =  0 a  =  9

Therefore,

a  =  9

b  =  -12 After having gone through the stuff given above, we hope that the students would have understood, how to find square root of a polynomial using long division.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 