Solving Quadratics

• In the past we have solved many equations of the form ax²+bx + c where a cannot equal to 0. 

• These are called linear equations and have only one solution. 

A quadratic equation

 an equation which can be written in the form  

ax²+bx + c = 0 

Where a, b, and c are constants, a  can’t 0. 

• A quadratic equation may have

• two, one-, or zero-real solutions. 

Whatever you do to one side,

you need to do to both 

• No negative number can be

• square rooted  

• x² cannot be less than

0 

• When there is no solution 

• no real solution 

• Square root property 

 

• square root both sides 

• When there is a square root,  

 

• put plus or minus to show the two solutions 

 

• Quadratic equatio

• n have two solutions, unless it is perfect square  

• Solve equations to singular x when there is only two terms and one term –

 

• x square = k 

• There can be a plus or minus square root = k and we do not expand

• – for perfect square 

• Number first than 

square root 

inverse property to

solve equation

• For quadratic equations which are not of the form x²,=k  

 

• Use alternative method of solution – Null factor 

 

Null factor law - 

factorise the quadratic and then apply the Null Factor law. 

• Get each side to equal 0 and

• get the factors 

• Then get two solutions from the two linear equations 

• – the possibilities 

• Do this by making the equation equal to 0 

• Firstly you can just factor out a common factor,

• PSN, perfect square, difference of two squares 

• If there is an variable outside the bracket,

• it is equal to 0 as a solution 

if there is an integer, it is

not included – factor out all possible common factors  

• Get rid of x² in this equation by

• square rootting. 

 

WARNING ON INCORRECT CANCELLING 

WARNING ON INCORRECT CANCELLING 

• Create perfect square, by

• removing the term that is not perfect to other side and adding in a new term