Chapter 3:
What is quadratic equation?
Quadratic equation is an equation where a high exponent of the variable (x) is a square, it is known to 2.
Formula: 2x2+5x-3 = 0
3:01 (Solution Using Factors)
This is one of the example of how to solve a problem
1. (x - 1) (x + 7) = 0
Answer:
1. If (x - 1) (x + 7) = 0 then either
x - 1 = 0 or x + 7 = 0
Final answer:
It can be x = 1 or x = -7
3:02 (Solution by Completing the Completing the Square)
This part completes an algebraic expression to form a perfect square, which the expression is (x + a)2 or (x - a)2.
This is one of the example of how to solve a problem
1. What must be added to the following to make a perfect square?
x2 - 5x
Answer:
1. Half of 8 is 4, so the perfect square is=
x2 + 8x + 4*2 = (x + 4)2
3:03 (The Quadratic Formula)
What is a quadratic Formula:
The quadratic formula is mainly used in algebra to solve a quadratic equations. The normal for of a quadratic equations is where "x" shows a variable, and a, b, and c are constants. A quadratic equations have 2 solutions which we can also call it roots.
3:04 (Choosing the Best Method)
Many quadratic equations appear in various different forms. They can always be simplified to the general form of ax2 + bx + c = 0.
This is one of the example of how to solve a problem
1. x(x - 5) = 6
Answer:
1. x(x - 5) = 6
x2 - 5x = 6
x2 - 5x - 6 = 0
Factorising gives:
(x - 6)(x + 1) = 0
x = 6 or -1
Chapter 5: Further Algebra
5:01 (Simultaneous Equations Involving a Quadratic Equation)
What is Simultaneous Equations Involving a Quadratic Equation?
Simultaneous Equations Involving a Quadratic Equation is how a solution of a linear equation and a quadratic equation is provided by a point (or more points) of intersection of the line and parabola representing the equations.
To find the solution, we need to eliminate y (or x) by substitution, and solve the quadratic equation though it's formed in x (or y). Then we can find the corresponding value of y or x.
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