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Question

# Find the discriminant of the equation and the nature of roots. Also find the roots, if they are real: 3x2âˆ’2x+13=0

A
Roots are imaginary
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B
D = 0, Roots are real and equal 13,13
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C
D= 25, Roots are real and unequal 15,12
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D
Cannot be determined
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Solution

## The correct option is C D = 0, Roots are real and equal 13,13 Nature of the roots of a quadratic equation is determined by its discriminant D=b2−4acComparing 3x2−2x+13=0 with ax2+bx+c=0 we get a=3,b=−2,c=13Therefore D=b2−4ac =(−2)2−4×3×13 =4−4 =0Therefore roots are real and equal.Therefore roots are, −b±√b2−4ac2a=−(−2)±√(−2)2−4×3×132×3=2±02×3=22×3=13Therefore roots are 13 ,13

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