xample 5 : Find the roots of the quadratic equation 3x? - 2/6x+2 = 0
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Given: 3x
2
−2
6
x+2=0
3x
2
−
6
x−
6
x+2=0,
3
x(
3
x−
2
)−
2
(
3
x−
2
)=0
(
3
x−
2
)(
3
x−
2
)=0∴
3
x−
2
=0 or
3
x−
2
=0
∴
3
x=
2
or
3
x=
2
,x=
3
2
or x=
3
2
So, the root is repeated twice, one for each repeated factor (
3
x−
2
)l.
∴ The two equal roots of 3x
2
−2
6
x+2=0 are
3
2
,
3
2
.
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