Solving Quadratic Equations

Home | Online Math Tutoring | Algebra1-Tutoring | Solving Quadratic Equations

The polynomial equation of second degree is called a quadratic equation.

The general form of quadratic equation is ax2 + bx + c = 0, where a, b, c are real numbers and.

We can solve quadratic equations by following methods –

1- Factorization

2- Completing the square

3- Using the quadratic formula

1) Factorization

In factorization we split the middle term into two parts such that the product of first term and the last term is equal to the product of the two splitted parts, then we perform grouping and at last we put both the brackets equal to zero to find out the required solutions.

Exampley2 + y – 2 = 0

                         Finding solutions of the given equation

                         y2 + 2yy – 2 = 0 (Splitting the middle term)

                         y(y + 2) – 1(y + 2) = 0

                         (y + 2) (y – 1) = 0 (Grouping)

                          Either (y + 2) = 0 or (y – 1) = 0

                           y = -2 or y = 1 are the required solutions.

2) Completing the square –

First we make coefficient of x2 as 1 by dividing the equation by a, then bring constant to the right side and then making left side perfect square by adding suitable constant both sides. After that we will take square root of both sides and finally we will solve for x.

  Example s2-3s-10=0


Using the Quadratic Formula:

First compare the given equation with the general equation ax2 + bx + c, then put the values of a, b, c in quadratic formula

Example -2x2+5x-6=0

 Putting value after comparing with general equation

Some facts about Quadratic Equations:

1) Any number when putting in place of variable if satisfies the equation is called the root of the equation.

2)  Zeros of  ax2 + bx + c and roots of ax2 + bx + c=0  are same.


Check point

Solve the following quadratic equations-

1) x2 + 15x + 56 = 0

2) a2 + 9a + 20 = 0

3) b2 + 2b – 4 = 0

4) y-(6/y) =5

5) p2 – 5p + 6 = 0


Answer Key

1)   -7, -8

2)    -5, -4

3)    -1+ squareroot(5), -1-squareroot(5)

4)      6, -1

5)       2, 3

Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.

Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.

Our ‘Learning by Design’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘What do you want to learn today?’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.

The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.

All tutoring sessions are recorded and made available for a month so you can review concepts taught.

Email or call our support team with any issues or questions – we are here for you 24X7.

Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!

Thousands have taken the eTutorWorld Advantage – what are you waiting for?

© 2020 eTutorWorld - Online Tutoring and Test Prep | All rights reserved

Memorial Day 10% Sale for ALL Tutoring and Practice Packs

Use coupon MEM10

Valid till May 31, 2020

You have Successfully Subscribed!