[Week 6]-Developing and applying the quadratic formula

[Week 6]-Developing and applying the quadratic formula
What I have learned:
Solving quadratic equations by determining square roots.
Solving by completing the square when a=1.
Solving by completing the square when a≠1.
Solving a problem using a quadratic equation.
Solving a quadratic equation of the form x^2+bx+c=0 .
Solving a quadratic equation of the form ax^2+bx+c=0 .
Using the quadratic formula to solve a problem.

Ex. Solve equation. Verify the solution.
2x^2-1=5
2x^2-1=5 Isolate the x^2-term.
2x^2=6 Divide each side by 2
x^2=3 Take the square root of each side.
X= ±√3
To verify, substitute each root in the given equation 2x^2-1=5 .
For x=√3,
L.S.= 2(√3)^2-1
=5

For x=-√3,

$ latex L.S.=  2(-√3)^2-1 $

=5
For each root, the left side is equal to the right side, so the solution is verified.

 

 

 

[Week 5]- Factoring Polynomial Expressions

[Week 5]- Factoring Polynomial Expressions
What I have learn:
Determining whether a given binomial is a factor of a given trinominal.
Factoring trinomials with rational coefficients
Factoring using a trinomial pattern.
Factoring using the difference of squares pattern.

Ex. Is d-4 a factor of each trinomial? Justify the answer.
2d^2+6d-56
Use logical reasoning.
If d-4 is a factor, then trinomial can be written as:
(d-4) (ad+b)
2d^2+6d-56 = (d-4) (ad+b) Expand
2d^2+6d-56 = ad^2-(4a+b)d-4b
The d^2 – terms on both sides must be equal.
a=2
-4b= -56,
So b= 9
The trinomial would be: (d-4)(2d+9)
Expand to check the d- term.
(d-4)(2d+9) = 2d^2+6d-56
since this trinomial is equal to the given trinomial, d-4 is a factor of the given trinomial.