GIVEN
x²+9x+20=0
a= 1 b= 9 c= 20
DISCRIMINANT
b²-4ac
(9)²-4(1)(20)
81-(80)= 1
NATURE OF ROOTS
Real Rational Unequal
x²+6x+13=0
a= 1 b= 6 c= 13
(6)²-4(1)(13)
(36)-52= -16
Not Real
3x²-5x= -4
3x²-5x+4=0
a= 3 b= -5 c= 4
(-5)²-4(3)(4)
(25)-48= -23
x²-2x-5=0
a= 1 b= -2 c= -5
(-2)²-4(1)(-5)
(4)+20= 24
Real Irrational Unequal
x²+8x+16=0
a= 1 b= 8 c= 16
(8)²-4(1)(16)
(64)-64= 0
Real Rational Equal
The discriminant is greater than Zero (d>0) and it is a Perfect square.
The discriminant is greater than Zero (d>0) but not a Perfect square.
The discriminant is equal to Zero.
The discriminant is less than Zero (d<0).
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Answers & Comments
Verified answer
ANSWER
GIVEN
x²+9x+20=0
a= 1 b= 9 c= 20
DISCRIMINANT
b²-4ac
(9)²-4(1)(20)
81-(80)= 1
NATURE OF ROOTS
Real Rational Unequal
GIVEN
x²+6x+13=0
a= 1 b= 6 c= 13
DISCRIMINANT
b²-4ac
(6)²-4(1)(13)
(36)-52= -16
NATURE OF ROOTS
Not Real
GIVEN
3x²-5x= -4
3x²-5x+4=0
a= 3 b= -5 c= 4
DISCRIMINANT
b²-4ac
(-5)²-4(3)(4)
(25)-48= -23
NATURE OF ROOTS
Not Real
GIVEN
x²-2x-5=0
a= 1 b= -2 c= -5
DISCRIMINANT
b²-4ac
(-2)²-4(1)(-5)
(4)+20= 24
NATURE OF ROOTS
Real Irrational Unequal
GIVEN
x²+8x+16=0
a= 1 b= 8 c= 16
DISCRIMINANT
b²-4ac
(8)²-4(1)(16)
(64)-64= 0
NATURE OF ROOTS
Real Rational Equal
CLASSIFICATION OF NATURE OF ROOTS
REAL RATIONAL UNEQUAL
The discriminant is greater than Zero (d>0) and it is a Perfect square.
REAL IRRATIONAL UNEQUAL
The discriminant is greater than Zero (d>0) but not a Perfect square.
REAL RATIONAL EQUAL
The discriminant is equal to Zero.
NOT REAL
The discriminant is less than Zero (d<0).
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