How do I solve a quadratic equation?

All quadratic equations can be written in the form ax2 + bx + c = 0, where a, b and c are constants. Firstly, check whether you can easily factorise the equation into the form (x + p)(x + q) = 0, where pq = c and p + q = b. If you can do this, then the roots of the quadratic equation are -p and -q. 

If the equation does not factorise nicely, then the quadratic formula can be used to find the roots of the equation. Again, write the equation in form ax2 + bx + c = 0. Then the quadratic formula is given by x = (-b +/- sqrt(b2 - 4ac))/2a. This will give us two roots to the equation if b2 - 4ac > 0, one root to the equation if b2 - 4ac = 0 and no roots if b2 - 4ac < 0. Use a calculator to find the value of the root(s).

MS

Related Maths GCSE answers

All answers ▸

How should I approach my GCSE maths paper?


C is a circle with equation x^2 + y^2 = 16. The point P = (3,√7) is on C. Find the equation of the tangent to C at the point P.


simplify (2q+4)/(p(p+1)) -q/p


There are 200 students in Year 10 110 are boys. There are 250 students in Year 11 140 are boys. Which year has the greater proportion of boys? (Taken from Nov 2014 AQA Unit 2)