CBSE Class 10 maths NCERT Solutions Quadratic Equations Ex 4.4 | nature of the roots

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Standard form of quadratic equation

First combine all the like terms in the quadratic equation.

Secondly, degree of each term must drop from left to right starting from 2.

Nature of roots

In the standard form of quadratic equation ax^2 + bx + c = 0, the value D=b^2-4ac is called Discriminant of quadratic equation.Based on Discriminant, we say real roots or not exist for a quadratic equation or not.Group of problems are solved on Nature of roots of quadratic equation.

Nature of roots of quadratic equation.

If Discriminant D greater than 0 then real roots exist.

If Discriminant D less than 0 then no real roots exist.

If Discriminant D=0 then roots are equal.

00:02 CBSE Class 10 maths NCERT Solutions chapter 10 Quadratic Equations Q1. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:(i) 2 x^2– 3 x + 5 = 0 (ii) 3 x^2 – 4 3 x + 4 = 0 (iii) 2 x^2 – 6x + 3 = 0

00:16 (i)

00:34 Discriminant of Quadratic Equation

01:10 Discriminant less than zero.No real roots exits.

01:25 (ii)

01:53 Detemine discriminant of Quadratic Equation

02:48 Apply quadratic formula

03:57 (iii)

04:24 Discriminant of Quadratic Equation

06:41 CBSE Class 10 maths NCERT Solutions chapter 10 Quadratic Equations Q2. Find the values of k for each of the following quadratic equations, so that they have two equal roots.(i) 2 x^2+ kx + 3 = 0 (ii) kx ( x – 2) + 6 = 0

07:18 Find discriminant

08:21 (ii)

09:07 Detemine discriminant (discriminant analysis) of Quadratic Equation

09:52 Word problems on Quadratic Equation (Problems based on mensuration)

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.

09:55 CBSE Class 10 maths NCERT Solutions chapter 10 Quadratic Equations Q3. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m^2? If so, find its length and breadth.

19:56 From step:1 10:10 From step:2 10:45 From step:3 11:06 From step:4

12:08 Word problems on Quadratic Equation (Problems based on Ages)

12:10 CBSE Class 10 maths NCERT Solutions chapter 10 Quadratic Equations Q4. Is the following situation possible? If so, determine their present ages.The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

12:11 From step:1 12:29 From step:2 13:43 From step:3 14:48 From step:4

15:49

15:52 CBSE Class 10 maths NCERT Solutions chapter 10 Quadratic Equations Q5. Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, findits length and breadth.

15:56 From step:1 16:02 From step:2 16:28 17:41 QUADRATIC FORMULA

Reference book for the above video is

National Council of Educational Research and Training (NCERT) Book for Class 10 Subject: Maths

This Video is also refers as CBSE Class 10 mathts NCERT Solutions Chapter 9 Quadratic Equations

This video is suited for CBSE Class 10 maths Quadratic Equations.

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