Type – Inequalities

Problem 1: , which is greater x or y?

Solution :

Problem 2: , which is greater x or y?

Solution:

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# Category: Quadratic Equations

## Quadratic Equation – Part 4

## Quadratic Equations – Part 3

#### Shortcut Method:

## Quadratic Equations- Part 2

#### Shortcut method:

#### Observe the diagram below

## Quadratic Equations – Part 1

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Type – Inequalities

Problem 1: , which is greater x or y?

Solution :

Problem 2: , which is greater x or y?

Solution:

Type 3:

Basic method:

To solve this problem in basic method we can use one formula

i.e. here a=42 b=97 c=56

By using this formula we can not solve this problem in less time. So to solve this problem in less time there an alternative method as shown below.

**Step 1**: Find the factors for first term 42

The factors are 2,3,6,7,42,1

6,7 are the appropriate factors for this case (See the below diagram for more details)

**Step 2:** Find the factors for constant 56

The factors are 2,3,7,8,56,1

7,8 factors are the appropriate factors for this case (See the below diagram for more details)

**Step 3:** Select 7 in the first one and 7 in the second one and multiply both

7*7=49

**Step 4:** Select 6 in the first one and 8 in the second one and multiply both

6*8=48

**Step 5:** Add both 49+48=97 which is equal to middle number i.e.97

**Step 6:** Divide the,

The result after the division –

**Step 7:** Change the sign

Observe the **diagram** for the given equation

Type 2:

Basic method:

- Step 1: Multiply the first number “2” and the constant 8
- 2*8=16

- Step 2: Find the factors for 16
- 2,4,8,16,1 are the factors.

- Step 3: Select the factors such that when we add we should get the middle number (8 in the given equation) and when we multiply we should get constant (16).
- 4 and 4 are such factors which will give sum as 8 and multiplication as 16.
- If we take 1 and 6, multiplication is 6 but the sum is 7 which is not equal to 5.
- So the appropriate factors for the given equation are 3 and 2.

- Step 4: Change the sign for the factors
- Since it is ”+8x” in the given equation we need to change the sign for the factors i.e. -4,-4
- If it is “-8x” in the equation we need to change the sign for the factor as 4, 4.

- Step 4: Divide the resultant factors by the first number 2
- are the final roots.

**Type 1: , **Find the roots for the equation?

Basic method:

Short Cut Method:

- Step1: Find the factors for constant (In the given equation it is 6)
- 2,3,6,1 are the factors for 6

- Step 2: Select the factors such that when we add we should get middle number (5 in the given equation) and when we multiply we should get constant (6).
- 2 and 3 are such factors which will give sum as 5 and multiplication as 6.
- If we take 1 and 6, multiplication is 6 but the sum is 7 which is not equal to 5.
- So the appropriate factors for the given equation are 3 and 2.

- Step 3: Change the sign for the factors
- Since it is ”+5x” in the given equation we need to change the sign for the factors i.e. -3,-2
- If it is “-5x” in the equation we need to change the sign for the factor as 3, 2.

Note: 2 and 3 are co-primes. So we should select co-prime factors.

Observe the below diagram