Question

Find the value of k for which the roots are real and equal in the following equation:

3x2 − 5x + 2k = 0

Answer 1

The given quadric equation is 3x² − 5x + 2k = 0, and roots are real and equal

Then find the value of k.

Here, a = 3, b = −5 and c = 2k

As we know that D = b² − 4ac

Putting the value of a = 3, b = −5 and c = 2k

= (−5)² − 4 × (3) × (2k)

= 25 − 24k

The given equation will have real and equal roots, if D = 0

Thus,

25 − 24k = 0

24k = 25

k = `25/24`

Therefore, the value of k = `25/24`.