Solving the quadratic equations using the FOIL method makes the equations easier for me to understand. The Foil method, multiplying the First, Outer, Inner and Last numbers, breaks down the equation a little further so you understand where some of your numbers are coming from, plus it helps me to check my work. Equation (a.) x^2 – 2x – 13 = 0

X^2 – 2x = 13 (step a)
4x^2 – 8x = 52 (step b, multiply by 4)
4x^2 – 8x + 4 = 52 + 4 (step c, add to both sides the square of original coefficient)
4x^2 – 8x + 4 = 56
2x + 2 = 7.5 (d, square root of both sides)
2x + 2 = 7.5 (e) 2x + 2 = -7.5 (f)
2x = 5.52x = -9.5
X = 2.75x = -4.75
(2x +2) (2x +2)
2x X 2x = 4x^2(foil method)
2x X 2 = 4x
2 x 2x = 4x
2 x 2 = 4
Simplify it 4x^2 – 8x + 4

I really got the hang of these equations by equation d and started enjoying figuring them out. I think the India method is an interesting method to solve equations and for me, I could understand it easier then some of the other methods we have been using. Using the formula X^2 –X + 41 to try if we can get a prime number was fun and interesting. I chose to use the numbers 0, 5,8,10, and 13, that is two even numbers and two...

...13 B) 51 + 2 3 13 C) 3 51 + 17 34 3 D) 51 - 2 3 19 B) x9 C) x18 D) 6x3 B) 4x + 29 C) -12x - 11 D) 12x + 29 B) -1 C) 0 D) 1
Find the product. 5) (x - 3)(x2 + 3x + 9) A) x3 - 6x2 - 6x - 27 B) x3 + 27 C) x3 - 27 D) x3 + 6x2 + 6x - 27
Factor the trinomial, or state that the trinomial is prime. 6) 20x2 + 23x + 6 A) (20x + 3)(x + 2) B) (4x - 3)(5x - 2) C) (4x + 3)(5x + 2) D) Prime
Factor completely, or state that the polynomial is prime. 7) 28x2 y - 28y - 28x2 + 28 A) (2y - 7)(7x - 2)(7x + 2) C) (7y - 7)(2x - 2)(2x + 2) Solve the system by the addition method. 8) 3x + 7y = 40 3x + 2y = 50 A) {(-2, 18)} Solve and check the linear equation. 9) 2x - 4 + 5(x + 1) = -2x - 3 A) {- 2} B) {4 } 3 C) {4 } 9 D) {- 6} B) {(-18, 3)} C) {(-18, 7)} D) {(18, -2)} B) (28y - 28)x2 + 4(-7y + 7) D) (28x2 - 28)y + 7(4 - 4x2 )
1
Solve the equation. x x 10) 27 - = 2 7 A) { 243 } 14 B) {42} C) {3} D) { 243 } 2
First, write the value(s) that make the denominator(s) zero. Then solve the equation. x-1 x+9 11) +3 = 4x x A) x ≠ 0; {34 } 3 5 B) No restrictions; { } 6 C) x ≠ 0, 4; { 37 } 9 D) x ≠ 0; { 37 } 9
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 12) 3(2x - 36) = 6x - 108 A) Identity Solve the problem. 13) You inherit $70,000 from a very wealthy grandparent, with the stipulation that for the first year,...

...QuadraticEquation:
Quadraticequations have many applications in the arts and sciences, business, economics, medicine and engineering. QuadraticEquation is a second-order polynomial equation in a single variable x.
A general quadraticequation is:
ax2 + bx + c = 0,
Where,
x is an unknown variable
a, b, and c are constants (Not equal to zero)
Special Forms:
* x² = n if n < 0, then x has no real value
* x² = n if n > 0, then x = ± n
* ax² + bx = 0 x = 0, x = -b/a
WAYS TO SOLVE QUADRATICEQUATION
The ways through which quadraticequation can be solved are:
* Factorizing
* Completing the square
* Derivation of the quadratic formula
* Graphing for real roots
Quadratic Formula:
Completing the square can be used to derive a general formula for solving quadraticequations, the quadratic formula. The quadratic formula is in these two forms separately:
Steps to derive the quadratic formula:
All QuadraticEquations have the general form, aX² + bX + c = 0
The steps to derive quadratic formula are as follows:
Quadraticequations and functions are very important in business...

...329
QuadraticEquations
Chapter-15
QuadraticEquations
Important Definitions and Related Concepts
1. QuadraticEquation
If p(x) is a quadratic polynomial, then p(x) = 0 is called
a quadraticequation. The general formula of a quadraticequation is ax 2 + bx + c = 0; where a, b, c are real
numbers and a 0. For example, x2 – 6x + 4 = 0 is a
quadraticequation.
2. Roots of a QuadraticEquation
Let p(x) = 0 be a quadraticequation, then the values of
x satisfying p(x) = 0 are called its roots or zeros.
For example, 25x2 – 30x + 9 = 0 is a quadraticequation.
3
And the value of x =
is the solution of the given
5
equation.
3
Since, if we put x =
in 25x2 – 30x + 9 = 0, we have,
5
2
3
3
LHS = 25 × – 30 ×
+ 9
5
5
= 9 – 18 + 9 = 0 = RHS
Finding the roots of a quadraticequation is known as
solving the quadraticequation.
5. Methods of Solving QuadraticEquation
( i ) By Factorization
This can be understood by the examples given
below:
2
Ex. 1: Solve: 25 x 30 x 9 0
Soln: 25x 2 30x 9 0 is equivalent to
5x 2 25x 3 32
0
5 x 32 0
3 3
3
,
or simply x
as the
5...

...Quadraticequation
In elementary algebra, a quadraticequation (from the Latin quadratus for "square") is any equation having the form
where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, the quadratic coefficient, the linear coefficient and the constant or free term.
Solving the quadraticequation
A quadraticequation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.
Factoring by inspection
It may be possible to express a quadraticequation ax2 + bx + c = 0 as a product (px + q)(rx + s) = 0. In some cases, it is possible, by simple inspection, to determine values of p, q, r, and s that make the two forms equivalent to one another. If the quadraticequation is written in the second form, then the "Zero Factor Property" states that the quadraticequation is satisfied if px + q = 0 or rx + s = 0. Solving these two linear...

...QUADRATICEQUATIONSQuadraticequations Any equation of the form ax2 + bx + c=0, where a,b,c are real numbers, a 0 is a quadraticequation.
For example, 2x2 -3x+1=0 is quadraticequation in variable x.
SOLVING A QUADRATICEQUATION
1.Factorisation
A real number a is said to be a root of thequadraticequation ax2 + bx + c=0, if aa2+ba+c=0. If we can factorise ax2 + bx + c=0, a 0, into a product of linear factors, then the roots of the quadraticequation ax2 + bx + c=0 can be found by equating each factor to zero.
Example – Find the roots of the equation 2x2 -5x +3=0, by factorisation.
Solution:
2x2 -5x +3=0 2x2 -2x-3x+3=0 2x(x-1)-3(x-1)=0 i.e., (2x-3)(x-1)=0 Either 2x-3=0 or x-1=0. So,the roots of the given equation are x=3/2 and x=1.
2. Completing the square
To complete the square means to convert a quadratic to its standard form. We want to convert ax2+bx+c = 0 to a statement of the form a(x h)2 + k = 0.
To do this, we would perform the following steps:
1) Group together the ax2 and bx terms in parentheses and factor out the coefficient a.
2) In the parentheses, add and subtract (b/2a)2, which is half of the x coefficient, squared.
3) Remove the term -...

...This article is about quadraticequations and solutions. For more general information about quadratic functions, see Quadratic function. For more information about quadratic polynomials, see Quadratic polynomial.
A quartic equation is a fourth-order polynomial equation of the form.
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.
Monomial – is a polynomial with only one term.
Binomial – is polynomial with two terms.
Trinomial – is a polynomial with four or more terms.
Polynomial – is a polynomial with three terms.
Constant – a polynomial of degree zero.
Linear – a polynomial of degree one
Quadratic – a polynomial of degree two
Cubic – a polynomial of degree three
Quartic – a polynomial of degree four
Quintic – a polynomial of degree five
Degree – is the highest exponents or the highest sum of exponents of the variables in a term
A population is all the organisms that both belong to the same group or species and live in the samegeographical area. In ecology the population of a certain species in a certain area is estimated using the Lincoln Index. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than...

...-------------------------------------------------
Primenumber
A primenumber (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a primenumber is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. This theoremrequires excluding 1 as a prime.
-------------------------------------------------
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of theintegers. Number theorists study primenumbers (which, when multiplied, give all the integers) as well as the properties of objects made out of integers (such as rational numbers) or defined as generalizations of the integers (such as, for example, algebraic integers).
Integers can be considered either in themselves or as solutions to equations (diophantine geometry). Questions in...

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