Using the quadratic formula solve quadratic equations | Word problems

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In this video, you will study quadratic equations, and various ways of finding their roots.A quadratic equations can be solved by any one the given methods (i)Method of completing the square (ii)Factoring quadratic equation (iii) Quadratic Formula.

Quadratic Formula is derived from Method of completing the square.To find roots of any quadratic equation by Quadratic Formula,we first need to find the Discriminant of quadratic equation.If Discriminant less than zero no real roots exist for given quadratic equation.If Discriminant is greater than zero, real roots exist.If Discriminant is zero then roots of quadratic equation are equal.

Solve the equation by Quadratic formula.

Steps to solve Word Problems:

Step 1:Read the problem carefully to know what is given and what to find out.

Step 2:Denote the unknown by a small letter like z, p etc.

Step 3:From the given condition, frame the quadratic equation Involving the unknown.

Step 4:Solve the equation by Quadratic formula.

Word problems on Quadratic Equation (Problems on Numbers)

00:02 Q4. The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3.Find his present age.

00:04 From step:1 00:16 From step:2 00:45 From step:3

01:06 How to write quadratic equation in standard form

02:37 Solve the quadratic equation by quadratic formula

04:45 Q5. In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

04:47 From step:1 5:15 From step:2 06:15 From step:3 08:08 solve by applying Quadratic formula

09:35 Q6. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

09:37 09:59 10:48 Pythagoras' Theorem Application:It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

11:09 Express quadratic equation in Standard form.

12:56 solution of quadratic equation by applying quadratic formula.

15:14 Q7. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

15:16 From step:1 15:30 From step:2 16:10 From step:3 17:00 From step:4

17:03 Quadratic formula

19:37 Q8. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

19:39 From step:1 19:55 From step:2 21:35 From step:3

21:44 Express in standard form of quadratic equation.

22:50 Quadratic formula

24:43 Q9. Two water taps together can fill a tank in 9 and 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

24:45 From step:1 25:06 From step:2 27:45 From step:3 30:52 Use quadratic formula.

34:00 Q10. An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains.

34:02 From step:1 34:30 From step:2 36:40 From step:3

37:14 Write quadratic equation in standard form

38:53 discriminant and nature of roots

39:30 Quadratic formula application

42:01 Q11. Sum of the areas of two squares is 468 m^2. If the difference of their perimeters is 24 m, find the sides of the two squares.

42:03 From step:1 42:21 From step:2 44:00 From step:3

45:51 nature of roots using discriminant

46:27 Quadratic formula

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