Page 71 - Math SL HB Sem 1

I.'TJNC'tIONS , EQU,,r'rroNS ,INIiQU;\L|TIUS

EQU,,rrIoNs

QtJA DITATIC EQIIA,I.tON

'lhe
general form ofa quadratic
a*O equation is atl + bx + c = 0, rvhere a, b, c are real constants and

IVIethods for solving quadratic equations

(i) Collect the terms in the order ax2 + hx ]- c = 0, then factorisc the Ieft_hand side

(2) Arrange in the form ax2 + bx--c,thencompletethesquareontheleft-hand

side, adding the appropriate number to both sides.
(.i) -b+ h) 4ac
=
Use the quadratic formula _r
2o
Thc Discriminant
'lhe
-
cxpression b2 4 ac is known as the discriminant and is often represented by the
delta symbol L=b2 4ac
-

The nature of the roots

(iiven
a quadratic function
f(x) = ax, + bx + c
-
Let A.= b'z 4ac then
,
(r) it A > 0, the equation
f(x) = O has two distinct real roots
(2) if A < 0 , the equation
.f(r) = O has two distinct complex roots.
(3) if A = 0, the equation (x) :0 has one repeated real root a
_
.f
2a

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