Question

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

2x² + kx + 3 = 0

In the following, determine the values of k for which the given quadratic equation has equal 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 × (2) × (3)

= k² - 24

∵ Roots of the given equation are real and equal

∴ D = 0

⇒ k² - 24 = 0

⇒ k² = 24

`rArrk=sqrt24`

`rArrk=+-sqrt(4xx6)`

`rArrk=+-2sqrt6`

Hence, the value of `k=+-2sqrt6`.