Find the best tutors and institutes for Class 10 Tuition
Q1(v):
Find the roots of the following quadratic equations by factorisation: (v) $100x^2 – 20x + 1 = 0$
Solution :
Given: A quadratic equation $100x^2 - 20x + 1 = 0$.
To find: The roots of the given quadratic equation using the method of factorisation.
Step 1: Identify the coefficients of the quadratic equation.
The standard form of a quadratic equation is $ax^2 + bx + c = 0$.
Comparing $100x^2 - 20x + 1 = 0$ with the standard form:
$a = 100$
$b = -20$
$c = 1$
Step 2: Determine the splitting of the middle term.
To factorise by splitting the middle term, we need to find two numbers such that:
1. Their product is equal to $a \times c = 100 \times 1 = 100$.
2. Their sum is equal to $b = -20$.
Let the two numbers be $p$ and $q$.
$p \times q = 100$
$p + q = -20$
Considering the factors of $100$: $(-10) \times (-10) = 100$ and $(-10) + (-10) = -20$.
Thus, the two numbers are $-10$ and $-10$.
Step 3: Rewrite the middle term and factorise by grouping.
Substitute $-20x$ with $-10x - 10x$ in the original equation:
$100x^2 - 10x - 10x + 1 = 0$
Group the terms into two pairs:
$(100x^2 - 10x) - (10x - 1) = 0$
Factor out the greatest common factor from each group:
$10x(10x - 1) - 1(10x - 1) = 0$
Step 4: Extract the common binomial factor.
$(10x - 1)(10x - 1) = 0$
This can be written as:
$(10x - 1)^2 = 0$
Step 5: Solve for $x$.
To find the roots, set the factor equal to zero:
$10x - 1 = 0$
$10x = 1$
$x = \frac{1}{10}$
Since the equation is a perfect square, both roots are identical:
$x = \frac{1}{10}, \frac{1}{10}$
Final Answer: The roots of the quadratic equation $100x^2 - 20x + 1 = 0$ are $\frac{1}{10}$ and $\frac{1}{10}$.
More Questions from Class 10 Mathematics Quadratic Equations EXERCISE 4.2
- Q1(i): Find the roots of the following quadratic equations by factorisation: (i) $x^2 – 3x – 10 = 0$
- Q1(ii): Find the roots of the following quadratic equations by factorisation: (ii) $2x^2 + x – 6 = 0$
- Q1(iii): Find the roots of the following quadratic equations by factorisation: (iii) $\sqrt{2}x^2 + 7x + 5\sqrt{2} = 0$
- Q1(iv): Find the roots of the following quadratic equations by factorisation: (iv) $2x^2 – x + \frac{1}{8} = 0$
- Q2: Solve the problems given below. Represent the following situations mathematically: (i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with. (ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs.750. We would like to find out the number of toys produced on that day.
- Q3: Find two numbers whose sum is $27$ and product is $182$.
- Q4: Find two consecutive positive integers, sum of whose squares is $365$.
- Q5: The altitude of a right triangle is $7$ cm less than its base. If the hypotenuse is $13$ cm, find the other two sides.
- Q6: 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.
CBSE Solutions for Class 10 Mathematics Quadratic Equations
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Quadratic Equations
Top Tutor
Bajaj Nagar, Nagpur
3 yrs of
Exp
1 student
Online Classes
Student's Home
Coaching is about improvising a student from where he/she is at. Not about converting an already bright student into an achiever. It should be obvious. The whole idea of ONE ON ONE coaching is to improvise and to elimate the problems in a detailed manner, exactly the way a student desires. To connect and respond to a student cannot be everybodys cup of tea. This is where a capable one comes in to fill the gaps where modern day educationalists fail to fill.
Top Tutor
Sector 92, Gurgaon
20 yrs of
Exp
10 students
1307 hrs of classes completed
900
per hour
Online Classes
Student's Home
Tutor's home
Teaching since last 20 years
Very friendly, patient, and clearly loves his job. highly recommend. barely anything negative to mention
Top Tutor
Kazipet, Warangal
2 yrs of
Exp
1 student
50 hrs of classes completed
Online Classes
Student's Home
Tutor's home
I have 5years of teaching experience where I implement Inductive ,Deductive teaching techinques in mathematics. I begin the teaching concepts of maths with basic level to high level which ensures the teaching learning process occurs even a below average student I make special work sheets for the brain nutrient students and also to the below average students ,so that helps students to become learn individually according to their level. In teaching maths concepts regarding Geometry , Trignometry and Areas and Circles here I use the concrete to semi concrete from thier i take them to abstract so child can easily familiar to the concept, teaching learning process occurs in a positive way. In teaching maths I use heuristic method which creates an enthusiasm among the students to learn maths subject and it eradicate the fear of maths from the students. As a teacher I teach according to the students taste and their interests, so teaching learning process will be occurred in a meaningful way. I observe the individual difference of the students while teaching, so that I can plan to teach according individual difference of the different students in the classroom. I use remedial class for the slow learners to develop in the subject. In this remedial session I mostly concentrating on the basic of maths subject so children can overcome the previous misunderstanding concepts regarding maths and here it will be taught his doubts regarding subject will be clarified. By teaching maths subject I make students all round development which is very valuable in the life.
Indirapuram, Ghaziabad
8 yrs of
Exp
3 students
300
per hour
Online Classes
Student's Home
I am a teacher of maths and science, having a experience of 8+ years in teaching, done my schooling from CBSe board and degree from IP university.
Top Tutor
Annamalai Colony, Chennai
8 yrs of
Exp
4 students
128 hrs of classes completed
400
per hour
Online Classes
Tutor's home
Tutor with experience teaching in math and science.Skilled at conveying complex knowledge in a simple and concise way.Looking to tutor school students and college students to achieve exceptional exam results. composed and implemented 40 high quality lesson plans.Composed and produced own lesson materials
Thank you so much mam, I loved your class very much, The class was very perfect. I understood the lesson very simple thank you mam.
Find more Tutor for Quadratic Equations in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
