Quadratic Equations

Sum of perfect cubes

a³ + b³ =(a + b) (a² - ab +b² )

Difference of perfect cubes

a³ - b³ = (a - b) (a² + ab + b² )

Quadratic equation

y= ax² + bx + c where a,b,c are real numbers are a= 0

One strategy to solve quadratics

factoring and it depends on zero product property

Completing square

1.) Isolate x and x² from constant c

2.) Factor out a (if a≠1)

3.) Take half of b, square it: (b/2)²

4.) Add this number to both sides.

5.)Factor the trinomial into a perfect square.

6.) Take the square root of both sides.

7.) Solve for x

when ax² +bx + c = 0 is solved by completing the square…

the quadratic formula is generated

quadratic formula

x = 2a−b± (square root b²−4ac​​)/ 2a

Discriminant

b² - 4ac in formula. allows to state how many real number solutions a quadratic equation has without solving it.

if b² - 4ac is negative

the equation has no real solution/ root

if b² - 4ac is zero

one real solution/ root

if b² - 4ac greater than zero

two real solutions/ root