find the coefficient of x² in Monic
quadratic equation
Answers
Answer:
In the module, Linear Equations we saw how to solve various types of linear equations. Such equations arise very naturally when solving elementary everyday problems.
A linear equation involves the unknown quantity occurring to the first power, thus,
for example,
2x − 7 = 9
3(x + 2) − 5(x − 8) = 16
= 8
are all examples of linear equations.
Roughly speaking, quadratic equations involve the square of the unknown. Thus, for example, 2x2 − 3 = 9, x2 − 5x + 6 = 0, and F2t2.pdf − 4x = 2x − 1 are all examples of quadratic equations. The equation F2t3.pdf = is also a quadratic equation.
The essential idea for solving a linear equation is to isolate the unknown. We keep rearranging the equation so that all the terms involving the unknown are on one side of the equation and all the other terms to the other side. The rearrangements we used for linear equations are helpful but they are not sufficient to solve a quadratic equation. In this module we will develop a number of methods of dealing with these important types of equations.
While quadratic equations do not arise so obviously in everyday life, they are equally important and will frequently turn up in many areas of mathematics when more sophisticated problems are encountered. Both in senior mathematics and in tertiary and engineering mathematics, students will need to be able to solve quadratic equations with confidence and speed. Surprisingly, when mathematics is employed to solve complicated and important real world problems, quadratic equations very often make an appearance as part of the overall solution.
The history of quadratics will be further explored in the History section, but we note here that these types of equations were solved by both the Babylonians and Egyptians at a very early stage of world history. The techniques of solution were further refined by the Greeks, the Arabs and Indians, and finally a complete and coherent treatment was completed once the notion of complex numbers was understood. Thus quadratic equations have been central to the history and applications of mathematics for a very long time.
Step-by-step explanation:
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Verified Answer :-
The coefficient is x is 2.
The number of monic quadratic polynomials of the form `x^2 + ax + b` with integer roots, where `1, a, b` are in `AP` is 2.
Step-by-step explanation:
Hence proved
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