Question

Find the nature of roots of the following equation 3x^2-2×+1/3=0 . If real roots exist find them

Answer 1

Answer:

• Roots are real and equal.

Step-by-step explanation:

• Compare given Quadratic equation

• with ax² + bx + c = 0 ,we get

• a = 3 , b = -2 , c = 1/3 ,

• Discreminant ( D ) = b² - 4ac

• = ( -2 )² - 4 × 3 × ( 1/3 )

• = 4 - 4

• = 0

Here, equation is , 3x2−2x+13=0

• Comparing it with, ax2+bx+c=0
• a=3,b=−2andc=13

So, discriminant,(d)=b2−4ac−−−−−−−√

d=(−2)2−4(3)(13)−−−−−−−−−−−−−−−√=0

We know, if d≥0, roots are real and if d<0, roots are unreal. Here, as

• d=0, roots are real and equal. Now, roots are=−b±d−−√2a=−b2a=13 So, roots are (13,13)

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