Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. See
[link] ,
[link] , and
[link] .
Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. See
[link] and
[link] .
Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation. The solution will yield a positive and negative solution. See
[link] and
[link] .
Completing the square is a method of solving quadratic equations when the equation cannot be factored. See
[link].
A highly dependable method for solving quadratic equations is the quadratic formula, based on the coefficients and the constant term in the equation. See
[link] .
The discriminant is used to indicate the nature of the roots that the quadratic equation will yield: real or complex, rational or irrational, and how many of each. See
[link].
The Pythagorean Theorem, among the most famous theorems in history, is used to solve right-triangle problems and has applications in numerous fields. Solving for the length of one side of a right triangle requires solving a quadratic equation. See
[link].
Section exercises
Verbal
How do we recognize when an equation is quadratic?
It is a second-degree equation (the highest variable exponent is 2).
When we solve a quadratic equation, how many solutions should we always start out seeking? Explain why when solving a quadratic equation in the form
$\text{\hspace{0.17em}}a{x}^{2}+bx+c=0\text{\hspace{0.17em}}$ we may graph the equation
$\text{\hspace{0.17em}}y=a{x}^{2}+bx+c\text{\hspace{0.17em}}$ and have no zeroes (
x -intercepts).
When we solve a quadratic equation by factoring, why do we move all terms to one side, having zero on the other side?
We want to take advantage of the zero property of multiplication in the fact that if
$\text{\hspace{0.17em}}a\cdot b=0\text{\hspace{0.17em}}$ then it must follow that each factor separately offers a solution to the product being zero:
$\text{\hspace{0.17em}}a=0\text{}or\text{b}=0.$
In the quadratic formula, what is the name of the expression under the radical sign
$\text{\hspace{0.17em}}{b}^{2}-4ac,$ and how does it determine the number of and nature of our solutions?
Describe two scenarios where using the square root property to solve a quadratic equation would be the most efficient method.
One, when no linear term is present (no
x term), such as
$\text{\hspace{0.17em}}{x}^{2}=16.\text{\hspace{0.17em}}$ Two, when the equation is already in the form
$\text{\hspace{0.17em}}{(ax+b)}^{2}=d.$
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
Y
master
X2-2X+8-4X2+12X-20=0
(X2-4X2)+(-2X+12X)+(-20+8)= 0
-3X2+10X-12=0
3X2-10X+12=0
Use quadratic formula To find the answer
answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x2-2x+8-4x2+12x-20
x2-4x2-2x+12x+8-20
-3x2+10x-12
now you can find the answer using quadratic
Mukhtar
2x²-6x+1=0
Ife
explain and give four example of hyperbolic function
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.