Algebra Notes

ALGEBRA

Quadratic equations:

An equation in which the highest power of the variable is 2. Thus, ax² + bx + c = 0, where a, b and c are constants.

There are three methods in solving a quadratic equation and they are:

a)      Factorization

Consider the equation c x d = 0, where c and d are constants. the product can only be 0 if c = 0,   d = 0 or both c and d = 0. 

b)      Using the quadratic formula

The solution to the equation ax² + bx + c = 0 is given by the formula: x = [-b±(√ b² - 4ac)]/2a

c)      Completing the square

Make the coefficient of x² = 1, followed by bringing the constant c to the right side of the equation,

then divide the coefficient by 2 and add the square to both sides of the equation. Finally, simplify b.

Solving inequalities

When an equality is multiplied or divided by a negative number, the inequality is reversed.

Eg. 4>-2, by multiplying this by -2,

-2(4>-2)= -8<4

Ordering:

= is equal to

≠ is not equal to

> is greater than

< is lesser than

≥ is greater than or 

Variation:

Direct Variation

y is proportional to x is written as y α x. 

y α x is also expressed as y =kx

Indirect Variation

y is inversely proportional to x is written as y α 1/x.

y α 1/x is also expressed as y = k/x