Question

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

2x² + kx + 3 = 0

Answer 1

The given equation is 2x² + kx + 3 = 0

The given equation is in the form of ax² + bx + c = 0

where a = 2, b = k and c = 3

Therefore, the discriminant

D = b² - 4ac

= k² - 4 x (2) x (3)

= k² - 24

∵ Roots of the given equation are real

∴ D ≥ 0

⇒ k² - 24 ≥ 0

⇒ k² ≥ 24

`rArrk>=sqrt24`

`rArrk>=+-sqrt(4xx6)`

`rArrk>=+2sqrt6`

or

`rArrk>=-2sqrt6`