Why does the discriminant b^2-4ac determine the number of roots of the quadratic equation ax^2+bx+c=0?

The rule for the discriminant: if b^2-4ac>0 then the quadratic has two roots if b^2-4ac=0 then the quadratic has one root if b^2-4ac<0 then the quadratic has no rootsRecall that the formula for solving the quadratic equation ax^2+bx+c=0 is x=(-b+(b^2-4ac)^0.5)/2a. Notice that the square-root of the discriminant is contained in this formula. If the discriminant is positive then it has a positive and negative square-root, giving two possible roots of the equation. If the discriminant is zero then this square-root term disappears giving only one root to the equation. Lastly, if the discriminant is negative then this square-root does not exist so the formula gives no answer.

DG
Answered by Dan G. Further Mathematics tutor

5876 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

What is the range of solutions for the inequality 2(3x+1) > 3-4x?


The equation of the line L1 is y = 3x – 2 The equation of the line L2 is 3y – 9x + 5 = 0 Show that these two lines are parallel.


What is the distance between two points with x-coordinates 4 and 8 on the straight line with the equation y=(3/4)x-2


How many different ways are there to seat 6 people at a round table?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning