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Question

# Find the discriminant of the equation and the nature of roots. Also find the roots.2x2−6x+3=0

A
D=12, Roots are real and distinct, x=3+32,332
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B
D=0, Roots are real and equal, x=3+32
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C
D=9, Roots are imaginary.
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D
None of these
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Solution

## The correct option is B D=12, Roots are real and distinct, x=3+√32,3−√32 Nature of the roots of a quadratic equation is determined by its discriminant D=b2−4acComparing 2x2+5√3x+6=0 with ax2+bx+c=0, we get a=2,b=−6,c=3Therefore, D=b2−4ac =(−6)2−4×2×3 =36−24 =12 >0Therefore roots are real.Therefore roots are,x=−b±√b2−4ac2a=−6±√(−6)2−4×2×32×2=6±√36−244=6±√124=6±√2×2×34=6±2√34=2(3+√3)4 and =2(3−√3)4=(3+√3)2 and =(3−√3)2

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