MYTUTOR SUBJECT ANSWERS

347 views

How to solve a quadratic equation?

 How to solve a quadratic equation?

While learning mathematics, you will often meet quadratic equations. These equations serve a mathematical way to say that a certain equation, which may resemble a real-life problem, may have more than one solution.

Identifying quadratics

The general formula of the quadratic is ax2 + bx + c = 0, but it is very rare that a quadratic equations appears in its very bare form. In exams, they often like to hide it in certain ways, for example:

·       5*cos2(x) + 3 = 2 *cos(x), where you can introduce a new variable y, and solve for y. Remember that you still need to solve for y = cos(x) after that.

·       Or basically they can use any trigonometric function or logarithm to hide a quadratic.

·       Often, a higher degree equation can be simplified to a quadratic, for example x6 + 3x3 + 2 = 0, where you can introduce a new variable, just like in the previous example.

Methods to solve a quadratic

The general formula for solving the quadratic is x = (-B + or – SQRT(B2 – 4AC))/2A

Where A, B,C are the coefficients of the equations. If you don’t know what a coefficient is, it is basically the number before the unknowns in the equation. Often you see can see that e.g. x2 doesn’t have a number before it, but that simply means that its coefficient is 1.

Also, you can use the Vieta-formulas to solve a quadratic, which are relationships between the coefficients of the equation and its roots (solutions).

-B/A = the two roots added together

C/A = the two roots multiplied together

I recommend that you get comfortable with these relationships, because these Vieta-formulas in some way remain true at higher degree equations.

Another method to solve a quadratic is, completing the square, for example x2 + 2x + 1 = (x+1)2, so we can know that -1 is the only solution to our quadratic equation.

Bence H. A Level Maths tutor, A Level Physics tutor, A Level Chemistr...

2 years ago

Answered by Bence, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

175 SUBJECT SPECIALISTS

£20 /hr

Manojhan S.

Degree: Mechanical Engineering (Masters) - Bath University

Subjects offered: Maths

Maths

“About Me: I am a Mechanical Engineering student at The University of Bath, where I am currently in my second year of the degree. I have found great enjoyment from learning about maths and science from my teachers and being able to app...”

MyTutor guarantee

£20 /hr

Riccardo P.

Degree: Physics (Bachelors) - Imperial College London University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Italian

“Hi, I'm Riccardo, a physics fresher at London's Imperial College from Milan. As you can imagine I really like physics and maths, but that doesn't mean I'll spend all my time studying! I'm an active guy who loves sports (boxing, diving ...”

MyTutor guarantee

£20 /hr

Jan K.

Degree: Mathematics and Music (Bachelors) - Edinburgh University

Subjects offered: Maths, Physics

Maths
Physics

“About Myself I am a Mathematics student at Edinburgh University. I have a real passion for Mathematics, and I thouroughly enjoy explaining mathematical concepts to others. Having been home-educated all through school (which also gave ...”

MyTutor guarantee

About the author

£20 /hr

Bence H.

Degree: Biomedical Engineering (Bachelors) - Imperial College London University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Computing
Chemistry

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

What's the deal with Integration by Parts?

The curve C has the equation y = 2x^2 -11x + 13. Find the equation of the tangent to C at the point P (2, -1).

Express (2x-1)/(x-1)(2x-3) in partial fractions.

What is a logarithm?

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok