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

2x^{2} + kx + 3 = 0

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#### Solution

The given equation is 2x^{2} + kx + 3 = 0

The given equation is in the form of

ax^{2} + bx + c = 0

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

Therefore, the discriminant

D = b^{2} - 4ac

= k^{2} - 4 x (2) x (3)

= k^{2} - 24

∵ Roots of the given equation are real and equal

∴ D = 0

⇒ k^{2} - 24 = 0

⇒ k^{2} = 24

`rArrk=sqrt24`

`rArrk=+-sqrt(4xx6)`

`rArrk=+-2sqrt6`

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

Concept: Nature of Roots

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