Recall:
QUADRATIC EQUATION
-an equation whose degree is 2
-an equation that can be written
2
in the form of ax + bx + c = 0,
where a, b and c
are all real numbers and a≠0
QUADRATIC EQUATION
2
ax
+ bx + c = 0
Note:
a, b and c are integers and a≠0
and a is expressed in terms of
positive integer.
SOLVING QUADRATIC EQUATION
A process of finding value/s for the variable(roots)
that will satisfy the quadratic equation.
There are 3 different ways on finding the roots of a
quadratic equation, these are (a) Extracting the root
(b)factoring, (c) completing the square and (d)
quadratic formula.
SOLVING QUADRATIC EQUATION
BY EXTRACTING THE ROOTS
This solution is intended for quadratic
equations whose value of b is 0.
STEPS:
ax2 + 0x + c = 0 or ax2 + c = 0
1. Put the constant term to the other side of the equation.
2. In case that the value of a is not 1, divide the given by
the value of a.
3. Get the square root of both sides of the equation.
4. Check the answer.
SOLVING QUADRATIC EQUATION
BY EXTRACTING THE ROOTS
Example1:
1. Find the roots/solution for
2
x
– 36 = 0
2
x
– 36 = 0
SOLVING QUADRATIC EQUATION
BY EXTRACTING THE ROOTS
Example 2:
2. What is the value of w that will make the
2
equation 3w = 27?
SOLVING QUADRATIC EQUATION
BY EXTRACTING THE ROOTS
Example 2:
3. Solve for the value of a in the equation
2
4a +7 = 71?
SOLVING QUADRATIC EQUATION
BY FACTORING (GCMF)
1. GCMF(Greatest Common Monomial Factor)used when the terms of the given has a
common factor. Usually this is applicable for
quadratic equation whose value of c is 0.
2
ax
+ bx = 0
SOLVING QUADRATIC EQUATION
BY FACTORING (GCMF)
STEPS:
2
ax
+bx = 0
1. Make sure that the given is in this form, ax2 +bx = 0
2. Factor the left side by the GCMF.
3. Use zero product property, equate each factor to 0
4. Solve each equation obtain from step 3.
5. Check the answer.
SOLVING QUADRATIC EQUATION
BY FACTORING (PST)
Factoring using PST ( Perfect Square Trinomial) is used
for any quadratic equation in the form of ax2 +bx +c = 0,
whose values of a and c are perfect squares. And the
middle term is twice the product of the square root of a
and c
2
2
X +4x + 4 = 0
4X -20x + 25 = 0
SOLVING QUADRATIC EQUATION
BY FACTORING (QTS)
Factoring using QTS ( Quadratic Trinomial Squares) is
used for any quadratic equation in the form of ax2 +bx
+c = 0, the factors can be done by trial and error
method.
2
2
X +5x + 6 = 0
3X -5x - 12 = 0