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 ▸

solve x/2 + 11 = 15


A ball, dropped vertically, falls d metres in t seconds. d is proportional to the square of t. The ball drops 45 metres in the first 3 seconds. How far does the ball drop in the next 7 seconds?


I’m having some trouble understanding functions. Mainly concerning how to know what the input and outputs are. Could you give me an explanation?


£X was invested for 5 years, earning compound interest of 2% per year. After 5 years the total value of the investment was £11,040.81. How do I calculate the value of the invested amount £X?