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

5548 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

Consider the Matrix M (below). Find the determiannt of the matrix M by using; (a) cofactor expansion along the first row, (b) cofactor expansion along the second column


Find dy/dx when y=2x^(4)+3x^(-1)


Find the stationary points of y=x^3 + 3x^2 - 9x - 4


Why does tanx = sinx/cosx ?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences