How do I solve a quadratic equation by factorising?
A quadratic equation is one that includes x2 as the highest power of x. Factorising is achieved in 3 steps. Let’s consider the example x2-3x-3=11) Put the equation into the form ax2+bx+c=0x2-3x-4=02) FactoriseWe need two numbers that- add together to get -3- Multiply together to get -4-4x1=-4 and -4+1=-3Thus, factorising gives (x-4)(x+1)=03) Solve the equation!If two numbers are multiplied together to give 0, one of them must be 0. Thus:x-4=0 and x=4x+1=0 and x=-1The equation has been solvedAdditional points:- This technique can be applied to finding the points of intersection on the x axis for a quadratic graph. For example, y=x2-3x-4. At the x axis, y=0 so you can work out x as above.- Harder quadratic equations can also be solved by factorising. For example when a isn't 1. 2x2 + 7x + 3=0Find two numbers that multiply to give 2x3 (6) and add to give 7. In this case, 6 and 1.Split 7x into 6x +x2x2 + 6x+x + 3=0Factorise each part by taking out a common factor. 2x(x+3)+1(x + 3)=0The sames as(2x+1)(x+3)=0thus x = -1/2 or x=-3Practice questions1. Solve by factorisingx2 + 6x + 8=0x2 – 8x + 16 = 02. Find the points of intersection with the x axis fory=x2 – 14x + 48and sketch this function
