Chapter 10 QuadratiC EQuations 369
EXAMPLES
Solve the quadratic equation with the quadratic formula.
2 x^2 + 3 x+ 1 = 0
We begin by observing a, b, and c: a = 2 b = 3 c = 1.
x=−± − =−± −
=−± =−+ −−
33421
22
398
4
31
4
31
4
31
4
()^2 ()()
()
, ==−−^2 =− −
4
4
4
1
2
,, 1
Solve the quadratic equation with the quadratic formula.
x^2 −x− 1 = 0 a= 1 b=− 1 c=− 1
x=−− ±−−−
= ±−− = ±+= ±
() () ()()
()
()
1141 1
21
114
2
114
2
15
2
22
15
2
15
2
= +−,
Solve the quadratic equation with the quadratic formula.
x^2 − 18 = 0 a = 1 b = 0 c=− 18
x=−± −−=±−−
=± =±⋅=±
0041 18
21
072
2
72
2
36 2
2
62
(^2) ()()
()
()
22
=± =−32 32 32,
Solve the quadratic equation with the quadratic formula.
2 x^2 + 6 x= 5
Rewrite as 26 xx^2 + – 50 = a = 2 b = 6 c = –5
x=−± −−^66425 =−± −− =−± =−± ⋅
22
63640
4
676
4
(^2) ()() 641
()
() 99
4
−± (^6219) = −± =−± =−+ −−
4
23 19
4
319
2
319
2
319
2
() ,
EXAMPLES
Solve the quadratic equation with the quadratic formula.
2
EXAMPLES
Solve the quadratic equation with the quadratic formula.