Formula of Discriminant: b²-4ac
EXAMPLES:
Given: x²+9x+20=0
Identify the values of a, b, and c:
a=1: b=9; c=20
b²-4ac
(9)²-4(1)(20)
81-160
D<0
Discriminant= -79
Nature of Roots: unreal/imaginary
a=1; b=6; c=13
(6)²-4(1)(13)
36-52
Discriminant= -16
Make it in standard form ax²+bx+c=0:
Standard form: 3x²-5x+4=0
a=3; b=-5; c=4
(-5)²-4(3)(4)
25-48
Discriminant= -23
a=1; b=-2; c=-5
(-2)²-4(1)(-5)
4+20
D>0
Discriminant= 24
Natur of Roots: real and unequal
a=1; b=8; c=16
(8)²-4(1)(16)
64-64
D=0
Discriminant= 0
Nature of Roots: real and equal
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Verified answer
Quadratic Equation:
Solve for the discriminant and identify its nature of roots
Formula of Discriminant: b²-4ac
EXAMPLES:
Given: x²+9x+20=0
Identify the values of a, b, and c:
a=1: b=9; c=20
b²-4ac
(9)²-4(1)(20)
81-160
D<0
Discriminant= -79
Nature of Roots: unreal/imaginary
a=1; b=6; c=13
b²-4ac
(6)²-4(1)(13)
36-52
D<0
Discriminant= -16
Nature of Roots: unreal/imaginary
Make it in standard form ax²+bx+c=0:
Standard form: 3x²-5x+4=0
a=3; b=-5; c=4
b²-4ac
(-5)²-4(3)(4)
25-48
D<0
Discriminant= -23
Nature of Roots: unreal/imaginary
a=1; b=-2; c=-5
b²-4ac
(-2)²-4(1)(-5)
4+20
D>0
Discriminant= 24
Natur of Roots: real and unequal
a=1; b=8; c=16
b²-4ac
(8)²-4(1)(16)
64-64
D=0
Discriminant= 0
Nature of Roots: real and equal