Question

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

x² - kx + 9 = 0

Answer 1

The given quadric equation is x² - kx + 9 = 0, and roots are real.

Then find the value of k.

Here, a = 1, b = -k and c = 9

As we know that D = b² - 4ac

Putting the value of a = 1, b = -k and c = 9

= (-k)² - 4 x (1) x (9)

= k² - 36

The given equation will have real roots, if D ≥ 0

⇒ k² - 36 ≥ 0

⇒ k² ≥ 36

`rArrk>=sqrt36` Or `k<=sqrt36`

⇒ k ≥ 6 Or k ≤ -6