082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

20 Chapter 1 Review of algebraic techniques
Inthe same way the binary equivalent ofthe decimal
number 0.5is 0.1.
5 (a) 91 16 =145 10 (b)6C =108 (c)2587 (d)63956
(e) 43981
6 (a) 160 10 = A0 (b)18C (c) 1392 (d)61A8
(e) F4240
7 (a)15 (b)255 (c)4095 (d)65535 (e)16 N −1
8 (a)101110111 2 (b)001101110101 bcd
9 (a)7F (b)157
1.4 POLYNOMIALEQUATIONS
Apolynomial equationhas the form
P(x) =a n
x n +a n−1
x n−1 +a n−2
x n−2 + ··· +a 2
x 2 +a 1
x +a 0
=0 (1.4)
where n is a positive whole number, a n
, a n−1
,...,a 0
are constants and x is a
variable. The constants a n
, a n−1
,...,a 2
, a 1
, a 0
are called the coefficients of the
polynomial.
The roots of an equation are those values ofxwhich satisfyP(x) = 0. So ifx =x 1
is a
rootthenP(x 1
) = 0.
Examples of polynomial equations are
7x 2 +4x−1=0 (1.5)
2x−3=0 (1.6)
x 3 −20=0 (1.7)
Thedegreeofanequationisthevalueofthehighestpower.Equation(1.5)hasdegree2,
Equation (1.6) has degree 1 and Equation (1.7) has degree 3. A polynomial equation of
degreenhasnroots.
Therearesomespecialnamesforpolynomialequationsoflowdegree(seeTable1.6).
Table1.6
Equation Degree Name
ax+b=0 1 Linear
ax 2 +bx +c = 0 2 Quadratic
ax 3 +bx 2 +cx+d=0 3 Cubic
ax 4 +bx 3 +cx 2 +dx +e =0 4 Quartic
1.4.1 Quadraticequations
Wenowfocusattentiononquadraticequations.Thestandardformofaquadraticequation
isax 2 +bx +c = 0.We look atthreemethods of solvingquadratic equations:
(1) factorization,
(2) use of a formula,
(3) completing the square.
Example 1.20 illustratessolution by factorization.