Question

the discriminant of 3x² - 2X + ⅓ is equal to zero​

Answer 1

Question:

Find the discriminant of the equation ;

3x² - 2x + 1/3 = 0 .

Answer:

D = 0

Note:

• An equation of degree 2 is know as quadratic equation .

• Roots of an equation is defined as the possible values of the unknown (variable) for which the equation is satisfied.

• The maximum number of roots of an equation will be equal to its degree.

• A quadratic equation has atmost two roots.

• The general form of a quadratic equation is given as , ax² + bx + c = 0 .

• The discriminant of the quadratic equation is given as , D = b² - 4ac .

• If D = 0 , then the quadratic equation would have real and equal roots .

• If D > 0 , then the quadratic equation would have real and distinct roots .

• If D < 0 , then the quadratic equation would have imaginary roots .

Solution:

The given quadratic equation is ;

3x² - 2x + 1/3 = 0

Clearly , we have ;

a = 3

b = -2

c = 1/3

We know that ,

The discriminant (D) of a quadratic equation is given as : b² - 4ac.

Thus,

=> D = (-2)² - 4•3•(1/3)

=> D = 4 - 4

=> D = 0

Hence,

The required value of the discriminant is 0 .

( moreover, the roots of the given quadratic equation will be equal as D = 0 )

Answer 2

$\huge{\boxed{\red{\star\;Answer}}}$

$\large{\underline{\blue{\star\;Note}}}$

$\boxed{\purple{Given\;equation\;3x^{2}-2x+\dfrac{1}{3}=0}}$

$\large{\underline{\green{\star\;Discriminent}}}$

If $ax^{2}+bx+c=0$ is a quadratic equation then

Discriminent is defined as follows

• $D=b^{2}-4ac$

1. If D > 0 , roots exist and they are real and distinct
2. If D = 0 , roots exist and they are equal
3. If D < 0 , roots are imaginery

$\underline{\purple{Calculating\;D\;of\;given\; equation\;3x^{2}-2x+\dfrac{1}{3}=0}}$

$D\;=b^{2}-4ac$

• Here,
• a = 3
• b = -2
• c = $\dfrac{1}{3}$

$D=b^{2}-4ac$

$D={-2}^{2}-4(3)(\dfrac{1}{3})$

$D=0$

$\large{\boxed{\red{The\;value\;D\;is\;0}}}$