Using Discriminants to Find the Number of Roots of a Quadratic Curve

In general, we could apply the formulax=\frac{-b\pm\sqrt{b^2-4ac\ }}{2a}. to work out the solutions of a quadratic function ax2+bx+c=0. 

The b2-4ac part is called the discriminant and the value of a discriminant could allow us to know the number of real roots that a quadratic function has. In other words, how many times does a quadratic curve cross the horizontal x axis in a graph?<o:p></o:p>

If b2-4ac=0, then a quadratic function has one real root and the graph of the function would be a curve just touch but not cross the x axis. In other words, the x axis is a tangent at the touching point and the touching point is also the minimum or maximum point of the function.<o:p></o:p>

If b2-4ac>0, then there are two real roots for the quadratic function and the corresponding graph would be a quadratic curve crosses over x axis twice.<o:p></o:p>

If b2-4ac<0, then there is no real roots for the quadratic function and a quadratic curve does not intersect or touch the horizontal axis at all in the graph. We could say that all points lying on this particular curve are either below the x axis or above the x axis.<o:p></o:p>

AL
Answered by Angela L. Maths tutor

5868 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A line has equation y = 2x + c and a curve has equation y = 8 − 2x − x^2, if c=11 find area between the curves


What is a hypothesis test


A curve has equation y = f(x) and passes through the point (4,22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7 use intergration to find f(x).


Find the exact value of x from the equation 3^x * e^4x = e^7


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