How do I find the roots of a quadratic equation?

There are a few methods you can use. Here are two methods: 1) Inspection. Say we have the equation x2+4x+3. We can find two numbers which multiply together to make 3 but add together to make 4. Such numbers are 3 and 1 (3*1=3 and 3+1=4). So we factorise this equation and it becomes (x+1)(x+3). To find the roots we make this equation equal to 0. This means that either (x+1)=0 or (x+3)=0, which implies that the roots are x=-1 and x=-3. 2) Quadratic Formula. For more complicated equations it makes sense to use the quadratic formula. For the general case, if we have ax2+bx+c then the quadratic formula says that the roots of this equation are (-b+sqrt(b2-4ac))/2a and (-b-sqrt(b2-4ac))/2a. This works for all quadratic equations provided that b2-4ac is non-negative. The number of roots depends on the value of b2-4ac.

DE
Answered by Daniel E. Maths tutor

3244 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

solve this simultaneous equation: 2x + 3y = 19 (Eq1) and 3x + y = 11 (Eq2)


The area of a parallelogram is given by the equation 2(x)^2+7x-3=0, where x is the length of the base. Find: (a) The equation of the parallelogram in the form a(x+m)^2+n=0. (b) The value of x.


Solve the following simultaneous equations: A. 2x-2y=18 and B. 3x+y=23


Solve this simultaneous equation using the process of elimination: -6x - 2y = 14 3x - 2y = 5


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