Equations & Inequalities Flashcards
How do you factorise a quadratic equation?
Step 1: Write the equation in the form ax^2 + bx + c = 0
Step 2: List out all factors of c, then choose two terms such that the sum of the factors equal b and the product equal c
How do you recognise the difference of two squares?
Its an expression with two terms, and both terms are squares, with a minus sign between them
How do you factorise difference of two squares?
(square root of 1st term + square root of 2nd term)(square root of 1st term - square root of 2nd term)
What is the first thing to do when solving factorising problems?
Always look for a common factor among all the terms.
How do you determine the nature of roots?
By using the discriminant which is equal to b^2 - 4ac
What are the steps involved in solving quadratic inequalities?
Step1: Factorise the quadratic
Step 2: Determine the critical values of x(x values of factorizing)
Step 3: Draw a number line with critical values indicated on the number line
Step 4: Test whether quadratic is + or - in the three regions of the number line by subbing any value in the region.
Step5: Write out your answer
How many ways are there to solve for simultaneous equations? Name all of them.
There are 3 ways
Substitution, elimination and graphically.
In solving simultaneous equations by substitution, what are the steps involved?
Step1: Use the simplest of the two given equations to express one of the variables in terms of the other.
Step 2: Substitute into the second equation
Step 3: Solve the second equation with the only one unknown variable
Step 4: Substitute the solved variable back into the first equation to obtain the value of the other unknown variable.
What is the value of the discriminant if roots are real and equal?
0
If the value of the discriminant is greater than 0, what does it mean?
It means roots are real and not equal.
