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

5086 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

Lengths of two sides of the triangle and the angle between them are known. Find the length of the third side and the area of the triangle.


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


Find the coordinates of the stationary points on the curve y=x^5 -15x^3


How can a system of two linear equations be solved?


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