Question

In the following determine the set of values of k for which the given quadratic equation has real roots:

4x² - 3kx + 1 = 0

Answer 1

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

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 roots, if D ≥ 0

⇒ 9k² - 16 ≥ 0

⇒ 9k² ≥ 16

⇒ k² ≥ 16/9

`rArrk>=sqrt(16/9)` or `k<=-sqrt(16/9)`

⇒ k ≥ 4/3 Or k ≤ -4/3