How to determine the number of unique real roots of a quadratic equation.

Take any quadratic equation, eg/ 3x2+4x-2=5, and rearrange to equal 0, ie/ 3x2+4x-7=0   (if you have an expression, ie/ there is no equals sign, then simply equate the expression to 0).

Now, we use the discriminant function, b2-4ac, of the quadratic, ax2+bx+c=0. Notice that a=3, b=4, and c=-7, in this case. This means that the discriminant is 42-43(-7)=16-(-84)=100. This is greater than 0. Therefore, there exist 2 unique real roots to our quadratic.

Simply put, if, for any quadratic of the form ax2+bx+c=0, that b2-4ac>0, then there exist 2 unique real roots, if b2-4ac=0 then there is 1 repeated real root, and if b2-4ac<0, then there are no real roots.

Answered by Yaniv P. Maths tutor

20477 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

3 1/2 - 2 1/3


In a school 2/5 students play an instrument. Of those students 3/7 play the violin. Find the ratio of students who play the violin compared to the students who do not play the violin.


Explain the use of the quadratic formula to solve quadratic equations.


How do you complete the square to answer quadratic equations?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences