Find the best tutors and institutes for Class 10 Tuition
Q1(ii):
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (ii) $3x^2 – 4\sqrt{3}x + 4 = 0$
Solution :
Given: A quadratic equation $3x^2 - 4\sqrt{3}x + 4 = 0$.
To Find: The nature of the roots and the roots themselves if they exist.
Step 1: Identify the coefficients of the quadratic equation.
The standard form of a quadratic equation is $ax^2 + bx + c = 0$. Comparing the given equation $3x^2 - 4\sqrt{3}x + 4 = 0$ with the standard form, we identify:
$a = 3$
$b = -4\sqrt{3}$
$c = 4$
Step 2: Determine the nature of the roots using the Discriminant ($D$).
The discriminant is given by the formula $D = b^2 - 4ac$.
Substituting the values identified in Step 1:
$D = (-4\sqrt{3})^2 - 4(3)(4)$
$D = (16 \times 3) - 48$
$D = 48 - 48$
$D = 0$
[Since $D = 0$, the quadratic equation has two equal real roots.]
Step 3: Calculate the roots using the Quadratic Formula.
The quadratic formula is given by $x = \frac{-b \pm \sqrt{D}}{2a}$.
Since $D = 0$, the formula simplifies to $x = \frac{-b}{2a}$.
Substituting the values:
$x = \frac{-(-4\sqrt{3})}{2(3)}$
$x = \frac{4\sqrt{3}}{6}$
Step 4: Simplify the expression.
$x = \frac{4\sqrt{3}}{6}$
Dividing both the numerator and the denominator by their greatest common divisor, which is $2$:
$x = \frac{2\sqrt{3}}{3}$
Since the roots are equal, both roots are $\frac{2\sqrt{3}}{3}$.
[Note: $\frac{2\sqrt{3}}{3}$ can also be written as $\frac{2}{\sqrt{3}}$ by rationalizing the denominator.]
Final Answer: The roots are real and equal, and the roots are $\frac{2\sqrt{3}}{3}, \frac{2\sqrt{3}}{3}$.
More Questions from Class 10 Mathematics Quadratic Equations EXERCISE 4.3
- Q1(i): Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) $2x^2 – 3x + 5 = 0$
- Q1(iii): Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (iii) $2x^2 – 6x + 3 = 0$
- Q2(i): Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots. (i) $2x^2 + kx + 3 = 0$
- Q2(ii): Find the values of $k$ for each of the following quadratic equations, so that they have two equal roots. (ii) $kx (x – 2) + 6 = 0$
- 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.
- 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 $48$.
- Q5: Is it possible to design a rectangular park of perimeter $80$ m and area $400$ $m^2$? If so, find its length and breadth.
CBSE Solutions for Class 10 Mathematics Quadratic Equations
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Quadratic Equations
Top Tutor
Anna Nagar Mullai Nagar, Chennai
9 yrs of
Exp
4 students
285 hrs of classes completed
500
per hour
Online Classes
With 9 years of experience in teaching 10th-grade mathematics both online and offline, I focus on delivering clear, concept-based lessons tailored to suit individual learning needs. By combining traditional teaching methods with digital tools, I create an interactive and engaging learning environment. My approach emphasizes understanding, regular practice, and personalized guidance, helping students gain confidence and excel in mathematics. I am committed to making mathematics enjoyable and accessible, ensuring every student progresses steadily toward academic success.
Her teaching is really great and understandable. I gained confidence for mathematics in board exams.
Super Tutor
Nerul Sector 20, Thane
10 yrs of
Exp
62 students
2884 hrs of classes completed
1200
per hour
Online Classes
I have done b.Tech in electrical engineering from IIT KANPUR. I taught one year in akash institute patna, 2 years in fiitjee patna. Currently I am teaching in unacademy. I have taught more than 6000 jee and neet aspirants. In which more than 500 students are selected in iitand aiims. If some one is interested to improve their physics upto jee advanced level take help with me .And see the magic. I can help students in their all type of assignment from any institute like allen, fiitjee, narayna, akash, resonance. I can help students to solve both volume of h.C verma within two month if some one is intrested in solving I.E.Irodov join me and see the next level of physics. My way of teaching is so easy and so advanced that student will realyy enjoy it. Don't waste your time in making decision just join and experience my level
He is a very dedicated teacher with excellent knowledge on topic. He knows Subject very well and teach accordingly to kids.
Top Tutor
Sector 19, Noida
3 yrs of
Exp
12 students
592 hrs of classes completed
Online Classes
• 3+ years of teaching experience. • teaching online tuitions of Mathematics for Class 10-12th. • pursued M.Sc. Mathematics from University of Delhi & B.Sc. Mathematical Sciences from University of Delhi. Passionate about solving mathematical problems and I have helped many students to overcome the fear of Maths.
Im so grateful that i got in contact with palak ma'am in my difficult phase.. my boards are on the end and she is standing with me to support me and help me till the end..thanks alot will make her proud for sure !! amazing teacher !! grateful
Top Tutor
Vimanapura Krishna Nagar, Bangalore
6 yrs of
Exp
3 students
666 hrs of classes completed
600
per hour
Online Classes
Student's Home
In this competitive world education is the most important tool rather I say that it is sword by which one can win the competition.so I am in this field from last four years and teaching is my passion and even strength.My students are very happy with me in college as well as in tutions. Their results show it all. Students are always been encouraged to do studies one should not force them for the same.
Top Tutor
Begur Road, Bangalore
5 yrs of
Exp
3 students
4 hrs of classes completed
300
per hour
Online Classes
Tutor's home
I have been teaching since last more than 5 years. My way of teaching style is so simple so that it make students very easier to understand. I am taking classes of Math, Hindi and Sanskrit subject.
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
