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Quadratic Equation Exercise 4.2

Hi Friends and Champs!

Before to begin next exercise, we need to understand some basic points, for solving the problems easily.

As you know the general equation for quadratic equation is:

ax2+bx+c=0, a ≠ 0

To factorize 

Step -1: Multiply coefficient of  x2  with constant term i.e. multiply "a" and "c".

Step-2: Factorize middle term or coefficient of x, such that the multiplication should be equal to the result obtained from multiplication of "a" and "c" and addition or subtraction should be equal to the middle term coefficient "b". 

Ex:    x2+5x+6=0 

Step -1: Multiply coefficient of x2  with constant term i.e. multiply "a" and "c",

                i.e. 1 x 6 =6

Step -2: 3 + 2 =5 (middle term coefficient)

              3 x 2 = 6 (multiplication of "a" and "c")

            now factor given equation like:

            x2+5x+6=0  

            x2+3x+2x+6=0

            x(x+3)+2(x+3)=0

            (x+2)(x+3)=0   (Hope you understand the method)

 

Middle term decision based on sign:

In ax2 + bx + c=0 , a ≠ 0  first sign "+" will break in ( + + ) i.e. +  in ++

In ax2 + bx - c=0 , a ≠ 0  first sign "+"will break in ( + - ) i.e. + in + -

In ax2 -  bx + c=0 , a ≠ 0  first sign "-" will break in ( - - ) i.e.  -  in - -

In ax2 - bx - c=0 , a ≠ 0  first sign  "-" will break in ( - + ) i. e.  - in - +

                                                            Exercise - 4.2

 1. Find the roots of the following quadratic equations by factorisation: 

(i) x2 – 3x – 10 = 0                         (ii) 2x2 + x – 6 = 0 

(iii) √2x2 +7x +5√2=0                 (iv) 2x2 – x + 1/8 = 0 

(v) 100x2 – 20x + 1 = 0

Solution:


2. Solve the problems given in Example 1. 

Solution: Pls see question 1 solution.

3. Find two numbers whose sum is 27 and product is 182.

Solution:


4. Find two consecutive positive integers, sum of whose squares is 365.

Solution :

5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides. 

Solution:


6. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ` 90, find the number of articles produced and the cost of each article.

Solution:





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