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

1.4 Polynomial equations 21
Example1.20 Solve
6x 2 +11x−10=0
Solution The left-hand side(l.h.s.)isfactorized:
(3x −2)(2x +5) =0
So either
3x−2=0 or 2x+5=0
Hence
x = 2 3 ,−5 2
When roots cannotbefound byfactorizationwecan make use ofaformula.
Theformulaforfindingthe roots ofax 2 +bx +c = 0 is
x = −b ± √ b 2 −4ac
2a
Example1.21 Usethe quadraticformulatosolve
3x 2 −x−6=0
Solution Comparing3x 2 −x−6 withax 2 +bx +cwesee thata = 3,b= −1 andc = −6.So
x = −(−1) ± √ (−1) 2 −4(3)(−6)
2(3)
= 1 ± √ 73
6
= −1.2573,1.5907
Engineeringapplication1.6
Currentusedbyanelectricvehicle
Personal transport systems that make use of electrical power are becoming increasinglycommon.Oneofthefactorsbehindthischangeisthattheirusecanreduceroadsidepollutioninanurbanenvironment.Electricalvehicleshavealsobecomethebase
forself-drivingcars when combinedwith electricalcontroland navigation systems.
The motor in an operational electric vehicle has to do work to overcome wind,
inertia, friction, road resistance and in order to climb inclines. The energy supply
in the form of electrical power comes from the on-board battery pack. Due to its
internal construction the battery pack has a total internal resistance,R, which serves
toreduce the power available tothe motor.
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