Determin the nature of root of following quadratic equation√3x^2 +√2x- 2√3=0
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11th
Maths
Complex Numbers and Quadratic Equations
Quadratic Equations
Find the nature of the root...
MATHS
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
(i) 2x
2
−3x+5=0
(ii) 3x
2
−4
3
x+4=0
(iii) 2x
2
−6x+3=0
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ANSWER
i)
x
2
−3x+5=0
a=2,b=−3,c=5
Discriminant, D=b
2
−4ac=9−40=−31
Since D<0, the roots are imaginary for the given equation.
ii)
3x
2
−4
3
x+4=0
a=3,b=−4
3
,c=4
Discriminant, D=b
2
−4ac=48−48=0
Since D=0, the roots are real and equal for the given equation.
3x
2
−4
3
x+4=0
a=3,b=−4
3
,c=4
x=
2a
[−b±
b
2
−4ac
]
x=
6
4
3
=
3
2
iii)
2x
2
−6x+3=0
a=2,b=−6,c=3
Discriminant, D= b
2
−4ac=36−24=12
Since D>0, roots are real but not equal.
x=
2a
[−b±
b
2
−4ac
]
x=
4
6±
12
x=
4
6±2
3
x=
2
3±
3