find the discriminant of the equation 3x2=5x+2=0 and hence write the nature of its roots
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Step-by-step explanation: D = 0, Roots are real and equal
3
1
,
3
1
Nature of the roots of a quadratic equation is determined by its discriminant D=b
2
−4ac
Comparing 3x
2
−2x+
3
1
=0 with ax
2
+bx+c=0 we get a=3,b=−2,c=
3
1
Therefore D=b
2
−4ac
=(−2)
2
−4×3×
3
1
=4−4
=0
Therefore roots are real and equal.
Therefore roots are,
2a
−b±
b
2
−4ac
=
2×3
−(−2)±
(−2)
2
−4×3×
3
1
=
2×3
2±0
=
2×3
2
=
3
1
Therefore roots are
3
1
,
3
1
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