QUADRATIC EQUATIONS

ALGEBRA:

QUADRATIC EQUATIONS.

Are equations where the highest exponent of variable  x is a square e.g x²

The Standard Form of a Quadratic Equation looks like this:

 

• a, b and c are known values. a can't be 0.

• "x" is the variable or unknown (we don't know it yet).

Here are some examples:

2x2 + 5x + 3 = 0		In this one a=2, b=5 and c=3
x2 − 3x = 0		This one is a little more tricky: Is this equation a quadratic equation? what is the value of ; a=?      b=?           c=?
5x − 3 = 0		Is this equation a quadratic equation?  what is the value of ; a=?      b=?           c=? SOLVING QUADRATIC EQUATIONS BY FACTORIZATION.   Product = C Sum = b When C is Positive (+) then two number all positive (+) or all negative (-). When C is negative, one number is a +and the other a - EXAMPLES: 1.        x² − 12x + 36  product = 36 , (-6 x- 6) Sum =  - 12 , (-6 + -6)               can be factored as (x − 6)(x − 6). (Roots) 2 .            2x² +5x + 3  product = 6, (3 x 2) Sum =  5,  (3+ 2) can be factored as? G 1) Factorize: x2 + 5x + 6  G 2)Factorize:  t2 + 2t - 24 G 3)Factorize: 2x2 + 6x + 4  G 4) Factorize: 4n2 + 12n + 9  Read more: http://www.mathwarehouse.com/sheets/algebra-2/quadratic-equation-worksheets/factoring-quadratic-equations-worksheet.php#ixzz5DWCr8DQa Problem 3.   Factorize the following equations in your groups.    G1)   x² − 3x + 2 G2)   x² + 7x + 12    G3)   x² + 3x − 10   G4)   x² − x − 30 (x + 5)(x − 6) x = −5  or  2. x = −5  or  6.    G1)   2x² + 7x + 3 G2)   3x² + x − 2 (2x + 1)(x + 3) (3x − 2)(x + 1) x = − 1 2   or  −3. x =  2 3   or  −1.    G3)   x² + 12x + 36 G4)   x² − 2x + 1 (x + 6)² A double root. A double root.