KOLEKSI SIRI PERTAMA QUANTUM COOL-ACTIVE: MATHEMATICS SIMPLIFIED : FROM BASICS TO BRILLIANCE

The type of roots of quadratic equations can be

determined from the values of b² - 4 ac which is

known as the discriminant

TYPES OF ROOTS INTYPES OF ROOTS IN (^)
QUADRATIC EQUATIONQUADRATIC EQUATION
SummarySummary
KeypointsKeypoints NotesNotes
EXAMPLE
The quadratic equation 푥² + k + 3 = k푥, where k is
a constant, has two equal real roots. Find the
possible values of k.
x²+ k + 3 = kx
x²- kx + k + 3 = 0
a = 1, b = -k and c = k+3
b² - 4ac = 0
(-k)² - 4 (1)(k+3) = 0
k² - 4k - 12 = 0
( k+2 )( k-6) = 0
k = -2 or k = 6
arranged the equation in
general form
a² + bx + c = 0
according to the type of
roots given in question
subtitute the values of a,b
and c
The roots of a
quadratic equation
are also called
the zeroes of
the equation.
The equation :
1 .has two real roots when the discriminant,
b² - 4 ac is greater than zero
2 .has two real roots when the discriminant is equal to zero.
3 .has two complex roots when the discriminant is less than zero.