Find the best tutors and institutes for Class 10 Tuition
Q1(v):
Check whether the following are quadratic equations : (v) $(2x β 1)(x β 3) = (x + 5)(x β 1)$
Solution :
Given: The equation $(2x - 1)(x - 3) = (x + 5)(x - 1)$.
To Find: Determine whether the given equation is a quadratic equation.
Definition: A quadratic equation in the variable $x$ is an equation of the form $ax^2 + bx + c = 0$, where $a, b, c$ are real numbers and $a \neq 0$.
Step 1: Expanding the Left-Hand Side (LHS)
The LHS is $(2x - 1)(x - 3)$. We apply the distributive property (FOIL method):
$(2x - 1)(x - 3) = 2x(x) + 2x(-3) - 1(x) - 1(-3)$
$= 2x^2 - 6x - x + 3$
$= 2x^2 - 7x + 3$ [Combining like terms $-6x$ and $-x$]
Step 2: Expanding the Right-Hand Side (RHS)
The RHS is $(x + 5)(x - 1)$. We apply the distributive property:
$(x + 5)(x - 1) = x(x) + x(-1) + 5(x) + 5(-1)$
$= x^2 - x + 5x - 5$
$= x^2 + 4x - 5$ [Combining like terms $-x$ and $5x$]
Step 3: Equating LHS and RHS and Simplifying
Now, set the expanded LHS equal to the expanded RHS:
$2x^2 - 7x + 3 = x^2 + 4x - 5$
To bring the equation into the standard form $ax^2 + bx + c = 0$, subtract $(x^2 + 4x - 5)$ from both sides:
$2x^2 - x^2 - 7x - 4x + 3 + 5 = 0$
$x^2 - 11x + 8 = 0$
Step 4: Verification against the Standard Form
The resulting equation is $x^2 - 11x + 8 = 0$.
Comparing this with the standard form $ax^2 + bx + c = 0$:
Here, $a = 1$, $b = -11$, and $c = 8$.
Since $a = 1 \neq 0$, the equation satisfies the condition for being a quadratic equation.
Final Answer: Yes, the given equation $(2x - 1)(x - 3) = (x + 5)(x - 1)$ is a quadratic equation.
More Questions from Class 10 Mathematics Quadratic Equations EXERCISE 4.1
- Q1(i): Check whether the following are quadratic equations : (i) $(x + 1)^2 = 2(x β 3)$
- Q1(ii): Check whether the following are quadratic equations : (ii) $x^2 β 2x = (β2)(3 β x)$
- Q1(iii): Check whether the following are quadratic equations : (iii) $(x β 2)(x + 1) = (x β 1)(x + 3)$
- Q1(iv): Check whether the following are quadratic equations : (iv) $(x β 3)(2x +1) = x(x + 5)$
- Q1(vi): Check whether the following are quadratic equations : (vi) $x^2 + 3x + 1 = (x β 2)^2$
- Q1(vii): Check whether the following are quadratic equations : (vii) $(x + 2)^3 = 2x (x^2 β 1)$
- Q1(viii): Check whether the following are quadratic equations : (viii) $x^3 β 4x^2 β x + 1 = (x β 2)^3$
- Q2(i): Represent the following situations in the form of quadratic equations : (i) The area of a rectangular plot is $528$ $m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
- Q2(ii): Represent the following situations in the form of quadratic equations : (ii) The product of two consecutive positive integers is $306$. We need to find the integers.
- Q2(iii): Represent the following situations in the form of quadratic equations : (iii) Rohanβs mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. We would like to find Rohanβs present age.
- Q2(iv): Represent the following situations in the form of quadratic equations : (iv) A train travels a distance of $480$ km at a uniform speed. If the speed had been $8$ km/h less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of the train.
CBSE Solutions for Class 10 Mathematics Quadratic Equations
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Quadratic Equations
Govindpuram, Ghaziabad
20 yrs of
Exp
1 student
34 hrs of classes completed
Online Classes
Student's Home
Tutor's home
I teach mathematics and science for class 10th students. In science I teach physics chemistry and biology. My aim is to teach the students in way so that they score 100percent in boards.
Top Tutor
Uttorayon Township, Siliguri
3 yrs of
Exp
3 students
91 hrs of classes completed
350
per hour
Online Classes
Student's Home
Tutor's home
Ability to connect with children (or with older students), on a personal level. communication and social skills.Teaching can be quite satisfying for people who do it well. I know this because I am a teacher, too. Although I do not think I'm always the best teacher, do I know that the majority of my students love me, and I guess this is partly why good things happen in my classroom. I have spent a lot of time thinking about and done a lot of research in to the question of what characteristics make a teacher effective and how I can succeed in the classroom. Although every great teacher has their own special, unique style, I have found that there are nine specific universal qualities that are necessary for anyone who wants to teach effectively, whether they want to teach in an elementary school or a university. If any teacher possesses the following characteristics and qualities, he/she can become a very good teacher with large fan base.
Top Tutor
Ujhani, Budaun
7 yrs of
Exp
5 students
502 hrs of classes completed
500
per hour
Online Classes
I am a TGT Maths teacher. I am giving online tution since 2019. I am certified in B.ed(Maths and Science). My key skills are problem solving, creativity and communication. I had an experience of 7 years in teaching ( Maths and Science).My accomplishments is to reorganized the things, innovations, practical learning and concept building and exploration of subject
Top Tutor
Kothanur, Bangalore
17 yrs of
Exp
18 students
552 hrs of classes completed
800
per hour
Student's Home
I am a Math and Hindi teacher with Aadya Academy, The World School Bangalore.I worked as a math and Hindi teacher with The Landmark school Rampura Bangalore for grades 7 to 10 for the last three years.I am an experienced, qualified teacher and tutor with over 17 years of experience in teaching Math and Hindi across different boards including CBSE, ICSE, and IGCSE for grade 7 to 12. I have 5 years of teaching experience with U. K based online company named FIRSTRING for GCSE, Edexcel and National curriculum of ENGLAND Syllabus . I am passionate about solving mathematical problems and helping students to understand easily. Over the years I have helped thousands of students overcome their fear of Math and Hindi Language.
Top Tutor
Roorkee, Roorkee
5 yrs of
Exp
6 students
80 hrs of classes completed
350
per hour
Online Classes
An experienced educator with over 5 years of teaching experience, I have had the privilege of mentoring more than 100 students. My expertise spans foundational high school courses (9thβ10th Science, 11thβ12th Biology) as well as advanced engineering disciplines (B.Tech & M.Tech). I hold a B.Tech, M.Tech, and Ph.D. in Biotechnology, alongside a competitive GATE qualification. My approach focuses on building deep conceptual clarity and critical thinking, followed by structured problem-solving, regular assessments, and rigorous PYQ practice. This exam-focused strategy ensures students achieve outstanding performance in both board exams and competitive tests.
Honestly, my experience at TTN Classes β Vigyan Classes has been really good π. Dr. Apoorva Singh Maβam teaches very well π and explains every concept in a simple and easy-to-understand way. Her classes are informative, interactive, and enjoyable π. She is very friendly and supportive with students π€, clears doubts patiently, and always motivates us to do better π―. She also gives career counselling and guidanceπ―, which really helps students understand their options and make better decisions about their future. I also really enjoy the celebrations π we have on different occasions like birthdays π, results π, and other events.These moments make the classes more memorable and create a great bond between students and teachers β€οΈ. Overall, I genuinely enjoy studying at Vigyan Classes. Great teaching π©βπ«, career guidance π―, a friendly environment π, and lots of memorable moments π. Definitely a great experience!
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
