Solving Quadratics and Exact Values

Solving Quadratic Equations by Factoring Let's solve the equation First you need to get it in what we call "quadratic form" which means need this to be 0 1 ok -18 So we have Now let's factor the left hand side Now set each factor = 0 and solve for each answer. ok

Extracting Square Roots The idea behind this method is when you have some "stuff" squared that you can get by itself on the left hand side of the equation (no other variables on the right hand side), you can then take the square root of each side to cancel out the square. Get the "squared stuff" alone which in this case is the t Now square root each side. Since you loose any negative sign when you square something, both the + and – of the number would solve the equation so you must do both.

Let's try another one Get the "squared stuff" alone which in this case is the u 2 44 Now square root each side and DON'T FORGET BOTH THE + AND – Remember with a fraction you can square root the top and square root the bottom

Another Example Get the "squared stuff" alone which in this case is the stuff in the brackets and it is alone. Now square root each side and DON'T FORGET BOTH THE + AND – Let's simplify the Surd 25 × 2 Now solve for x 22

One Last Example Get the "squared stuff" alone which in this case is the stuff in the brackets. Now square root each side and DON'T FORGET BOTH THE + AND – This will give you an i Now solve for y Year 12 Calculus

Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. Shawna has kindly given permission for this resource to be downloaded from and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar