Question

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

4x² - 3kx + 1 = 0

Answer 1

The given quadric equation is 4x² - 3kx + 1 = 0, and roots are real and equal

Then find the value of k.

Here, a = 4, b = -3k and c = 1

As we know that D = b² - 4ac

Putting the value of a = 4, b = -3k and c = 1

= (-3k)² - 4 x (4) x (1)

= 9k² - 16

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

Thus,

9k² - 16 = 0

9k² = 16

k² = 16/9

`k=sqrt(16/9)`

`k=+-4/3`

Therefore, the value of `k=+-4/3` .