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Title: Algebra _ Computation of square root
Description: Algebra _ Computation of square root COMPUTATION OF SQUARE ROOT The square root of a given number is another number which when multiplied with itself results in the given number. Similarly, the square root of a given polynomial P(x) is another polynomial Q(x) which when multiplied by itself gives P(x). In the earlier classes you learnt to find square root of polynomials by factorisation method. Here, we find square root by the method of division. For polynomials of higher degree the method of division is very much useful. This method is similar to the division method of finding the square root of numbers.
Description: Algebra _ Computation of square root COMPUTATION OF SQUARE ROOT The square root of a given number is another number which when multiplied with itself results in the given number. Similarly, the square root of a given polynomial P(x) is another polynomial Q(x) which when multiplied by itself gives P(x). In the earlier classes you learnt to find square root of polynomials by factorisation method. Here, we find square root by the method of division. For polynomials of higher degree the method of division is very much useful. This method is similar to the division method of finding the square root of numbers.
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Algebra
Computation of square root
I
...
(a) 4x4 12x3 + 37 x2 – 42x + a
4x4 12x3 + 37x2 – 42x + a is a perfect square, to find a
Solution:
2
2
3
+7
4
4
12
37
43
4
6
12
12
7
– 42
a
42
42
a
49
37
9
28
28
0
a = 49
(b) x4 4x3 + 10x2 – ax + 9
x4 4x3 + 10x2 – ax + 9 is a perfect square, to find a
Solution:
1
22
24 +3
1
2
+3
1
1
4
10
4
4
10
4
6
6
–a
a
12
0
9
9
9
a = 12
III
...
(a) x4 + 4x3 + 16x2 + ax + b
Solution:
x2 + 2x + 6
x2
2x2 + 2x
x4 + 4x3 + 16x2 + ax + b
x4
4x3 + 16x2
4x3 + 4x2
2x2 + 4x + 6
12x2 + ax + b
12x2 + 24x + 36
0
a = 24
b = 36
(b) 49x4 70x3 + 109x2 + ax b
Solution:
49x4 70x3 + 109x2 + ax b is a perfect square, to find a and b
...
– 1
1
1
1
–5/4
2
3/2
2
2
3/2
+1
a
b
1
2–1
2 – 2
5
2
5/2
5/2
+a
+ 5/2
+ b
+ 25/16
0
a = 5/2 ;
(d)
1
6
13
3 + 2 +
x4
x
x
a
+ b
x
Solution:
1
2–3
2–6+2
1
1
b = + 25/16
1
3
+2
6
13
a
6
6
13
9
4
4
a
12
0
a = 12 ; b = 4
b
b
4
Title: Algebra _ Computation of square root
Description: Algebra _ Computation of square root COMPUTATION OF SQUARE ROOT The square root of a given number is another number which when multiplied with itself results in the given number. Similarly, the square root of a given polynomial P(x) is another polynomial Q(x) which when multiplied by itself gives P(x). In the earlier classes you learnt to find square root of polynomials by factorisation method. Here, we find square root by the method of division. For polynomials of higher degree the method of division is very much useful. This method is similar to the division method of finding the square root of numbers.
Description: Algebra _ Computation of square root COMPUTATION OF SQUARE ROOT The square root of a given number is another number which when multiplied with itself results in the given number. Similarly, the square root of a given polynomial P(x) is another polynomial Q(x) which when multiplied by itself gives P(x). In the earlier classes you learnt to find square root of polynomials by factorisation method. Here, we find square root by the method of division. For polynomials of higher degree the method of division is very much useful. This method is similar to the division method of finding the square root of numbers.