Question

1
18. Find the discriminant of the equation
3x2 - 2x +
+ = 0 and hence find the nature
of its roots. Find them, if they are real.
3​

Answer 1

Correct Question :

• Find the discriminant of the equation 3x² - 2x +1/3= 0 and hence find the nature of its roots. Find them, if they are real.

Answer :

• The roots of equation are 1/3 , 1/3

To find :

• Nature of roots

Solution :

➞ 3x² - 2x + 1/3 = 0

➞ 3 × 3x² - 3 × 2x + 1 / 3 = 0

➞ 9x² - 6x + 1 = 0 × 3

➞ 9x² - 6x + 1 = 0

Now, Comparing equation with ax² + bx + c = 0 (Quadratic equation) we get,

• 9x² - 6x + 1 = 0

Where,

• a = 9
• b = - 6
• c = 1

We know that,

• D = b² - 4ac

➞ D = b² - 4ac

➞ D = (-6)² - 4 × 9 × 1

➞ D = 36 - 36

➞ D = 0

• D = 0 , two equal real roots

D = 0 Given equation has two equal real roots so,

Now, we have to use the qudratic equation formula to find the roots

We know that

• x = -b ± √D / 2a

Now Putting the value we get,

➞ x = -b ± √D / 2a

➞ x = (-6) ± √0 / 2 × 9

➞ x = 6 + 0 / 18

➞ x = 6/18

➞ x = 1/3

Hence, The roots of equation are 1/3 , 1/3

More Explanation :

• D < 0 , no real roots
• D = 0 , two equal real roots
• D > 0 , two distinct real roots