1. What is the characteristic properties of one ?
  2.  What is the general form of q when decimal expansion of p/q is terminating ?
  3. What is the general form of q when decimal expansion of p/q is non-terminating &reccuring ? 
  4. Write the steps to solve a quadrati equation by the method of completing the square. 
  5. What is the formula to find LCM & HCF of p,q,r,when p,q,r are given. 

Asked by sureshchp | 12th Jun, 2019, 09:27: PM

Expert Answer:

1. Properties of One:

i. Multiplying any number by 1 does not change the value of the number.

Examples:

8 × 1 = 8

-2 × 1  = -2 

0 × 1 = 0

ii. Dividing any number by 1 does not change the value of the number.

Examples:

8 ÷1 = 8

-2 ÷ 1  = -2 

0 ÷ 1 = 0

2. 

Note: p and q should be co-prime mean HCF(p, q) = 1

If the prime factorisation of q is in the form of 2n 5m , where m and n are non negative integers then p/q have termination decimal expansion.


3. 

If the prime factorisation of q is not in the form of 2n 5m , where m and n are non negative integers then p/q is non - termination recurring.

4. 
The steps involved in solving a quadratic equation by completing the square method are as follows:
Step 1: Make the coefficient of x2 unity.
Step 2: Express the coefficient of x in the form 2 ×x ×p.
Step 3: Add and subtract the square of p.
Step 4: Use the square identity (a + b)2 or (a - b)2 to obtain the quadratic equation in the required form (x+a)2 - b2 =0. Then, take the constant term to the other side of the equation.
Step 5: Take the square root of the obtained equation to get the roots of the given quadratic equation. 
 
5.

For finding LCM and HCF of the given number, there is not a specific formula.

i. First find the prime factorisation of all given numbers.

HCF = common factor/s  (of all the given numbers) if not then 1 is the HCF.

LCM = common factor/s × uncommon factor/s 

 

Answered by Yasmeen Khan | 13th Jun, 2019, 10:54: AM