Page 71 - Math SL HB Sem 1

r,'tJNC',tI0Ns , FrQU.^',r'l oNS, INrtQt.r,.\LtTr
-__- !ts

IiQtJz\I IONS

QUAI)ILATIC T'QUA'TION

'lhe
a*0.
general form of a quadratic equation is rr- + bx+ c = 0, rvhere a, b, c are real constants and
ll{ethods ftrr solving quadratic equations

(r) collect the terms in the order ax2 + bx + c = 0, then factorise the left-hancr sirre

(2) Arrange in the lorm ax2 + bx
= -c , then complete the square on the left_hand
side, adding lhe appropriate number to both sides.
(3) -b+ b2 4ac
-
Use the quadratic formula x
=
2a
Thc Discriminant

-
The expression b2 4 ac is known as the discriminant and is often represented by the
clelta symbol A-b2 - 4ac

The nature of the roots

(iiven
f
=
a quadratic function (r) ax, + bx + c
Let A=62 -4ac,then
(l) il A > 0, the equation
f(r) = O has two distinct real roots.
(2) if A < 0 , the equation
f(x) = O has two distinct complex roots.
(3) if A - 0, the equation = 0 has one repeated real root b
"f(x)
2a

)- t6