) For what value of 'k', the pair of linear equations kx + 3y Find the discriminant of the quadratic equation 3x²-5x+2=0
and hence write the nature of its roots.
Answers
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Class 11
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>>Find the discriminant of the equation an
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Find the discriminant of the equation and the nature of roots. Also find the roots, if they are real:
3x
2
−2x+
3
1
=0
Medium
Solution
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Correct option is B)
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