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

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / Using Discriminants to Find the Number of Roots of a Quadratic Curve

641 views

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

In general, we could apply the formula $x=\frac{-b\pm\sqrt{b^2-4ac\ }}{2a}.$ 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?

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.

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.

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.

Angela L. GCSE Maths tutor, A Level Maths tutor

3 years ago

Answered by Angela, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

421 SUBJECT SPECIALISTS

Sobia K. A Level Further Mathematics tutor, A Level Maths tutor, GCS...

View profile

£24 /hr

Sobia K.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Spanish+ 1 more

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

5.0

16 reviews | 85 completed tutorials

Save profile

Rhianna C. 13 Plus Maths tutor, GCSE Maths tutor, A Level Maths tuto...

View profile

£20 /hr

Rhianna C.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Chemistry+ 1 more

“I am currently studying Maths at University and absolutely love it! I can't wait to share my enthusiasm with you!”

5.0

1 review | 8 completed tutorials

Save profile

Scott R. GCSE Maths tutor, 13 Plus Maths tutor, A Level Maths tutor,...

View profile

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

5.0