Calculators

We all have scientific calculators and we all know how to use it. It is indeed simple to use. However, when it comes to specific laws in mathematics, like Algebra, the buttons you press may vary different answers to the right one. So in this article I hope everyone will be more aware and careful!

How to Use a Scientific Calculator for Algebra?

Various functions are provided to understand how to use a scientific calculator for Algebra:
Generally scientific calculators are more featured than standard four or five-function calculator, and this difference is clearly seen in the type of manufacturers and models; however, the main features of scientific calculators are:
scientific notation
Arithmetic including floating Point numbers
logarithmic functions
trigonometric functions
exponential functions
roots can be calculated other than Square root
quick access to constants like P and e

Uses of scientific calculators:
Quick access to mathematical functions is possible with scientific calculators, functions like those related to Trigonometry; the situations involving direct calculations of very large numbers (such as in contexts of astronomical calculations). In schools also the use of scientific calculators is a usual thing, having solved the problems of maths and physics.
An Example can be taken to understand the use of scientific calculators:Q.For example, how would you solve 10 = x^2 + 3*(x ^1) using scientific calculator?
Solution: All the above used operations are present in the scientific calculators which directly calculate the value of ‘x’ solving the algebraic equation:
x ^ 2 + 3* (x ^1) – 10= 0
x = 5 or -2

Try It!

As a follow up from my previous post about Quadratic Equations, try out these questions and test your knowledge!

1.	Solve for y:  y2 - 81= 0 2. Solve for m:   m2 = 7m 3. Solve for x:  x2 - 3x - 10 = 0 4. Solve for y:  2y2 + 4 = 9y

Now try these harder questions! 

6.	Solve for x:     7. Solve for x:     8.    During practice, a softball pitcher throws a ball whose height can be modeled by the equation h = -16t 2  + 24t +1, where h = height in feet and t = time in seconds.  How long does it take for the ball to reach a height of 6 feet?

May the right answers be with you!

Quadratic Equations

What is it?

In elementary algebra, a quadratic equation (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 islinear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.^[1]

Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two.

Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorising, by completing the square, by using thequadratic formula, or by graphing. Solutions to problems equivalent to the quadratic equation were known as early as 2000 BC.

Quadratic Factorisation

The term

${\displaystyle x-r}$

is a factor of the polynomial

${\displaystyle ax^{2}+bx+c}$

if and only if r is a root of the quadratic equation

${\displaystyle ax^{2}+bx+c=0.}$

It follows from the quadratic formula that

${\displaystyle {\begin{aligned}ax^{2}+bx+c&=a\left(x-{\frac {-b+{\sqrt {b^{2}-4ac}}}{2a}}\right)\left(x-{\frac {-b-{\sqrt {b^{2}-4ac}}}{2a}}\right)\\&=a\left(x+{\frac {b-{\sqrt {b^{2}-4ac}}}{2a}}\right)\left(x+{\frac {b+{\sqrt {b^{2}-4ac}}}{2a}}\right).\end{aligned}}}$

In the special case b² = 4ac where the quadratic has only one distinct root (i.e. the discriminant is zero), the quadratic polynomial can be factored as

${\displaystyle ax^{2}+bx+c=a\left(x+{\frac {b}{2a}}\right)^{2}.}$