Question

Find the discriminant of the equation 3×2– 2x +1/3= 0 and hence find the nature of its roots. Find them, if they are real.​

Answer 1

⠀⠀ıllıllı uoᴉʇnloS ıllıllı

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Here,

• a = 3
• b = - 2
• c = 1/3

Since, Discriminant = b2 - 4ac

= (- 2)2 - 4 × 3 × 1/3

= 4 - 4 = 0.

Hence, the given quadratic equation has two equal real roots.

The roots are -b/2a and -b/2a.

2/6 and 2/6

or

1/3, 1/3

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Answer 2

Answer:

discriminant value b^2 -4ac

(-2)^2 - 4×3×1/3

4-4

=0

the roots are real & equal

the given equation is ,

3X^2-2X+1/3

so ,

-b/2a are the roots

-(-2)/2×3

2/6

=1/3