Discriminate
Discriminate means to make difference.but in mathematics we use discriminate formula to find the nature of the roots of quadratic equation without solving the quadratic equation.
Discriminate formula
D = b2 - 4ac
where ,
D = Discriminate
a,b and are the coefficients
c is content term of quadratic equation
where ,
D = Discriminate
a,b and are the coefficients
c is content term of quadratic equation
Rules for nature of root of quadratic equation
If discriminate is zero (D = O) then the roots of this equation are real and equal.
If discriminate is in negative (D = - answer) then roots of this equation are unequal and imaginary.
If discriminate is positive and perfect square then roots of this equation are real,unequal and rational.
If discriminate is positive but not perfect square then roots of this equation are real,unequal and irrational.
examples
1- 4x2+ 3x+2=0
solution
a=4 , b=3 , c=2
D = b2 - 4ac put the values in formula
D = (3)2 - 4(4)(2)
D = 9-32
D = -23
D = negative so root of this equation are unequal and imaginary.
2- 3x2+ 5x-1=0
solution
a=3 , b=5 , c=-1
D = b2 - 4ac put the values in formula
D = (5)2 - 4(3)(-1)
D = 25+12
D = 37
D = positive but not perfect square that why roots of this equation are real,unequal and irrational.
3- -x2+ 2x-1=0
solution
a= -1 , b= 2 , c= -1
D = b2 - 4ac put the values in formula
D = (2)2 - 4(-1)(-1)
D = 4-4
D = 0
D = 0 so the roots of this equation are real and equal.
4- x2+ 5x-6=0
solution
a= 1 , b= 5 , c= 6
D = b2 - 4ac put the values in formula
D = (5)2 - 4(1)(6)
D = 25-24
D = 1
D = positive and perfect square so roots of this equation are real,unequal and rational.
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