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Question
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
Solution
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 and equal
∴ D = 0
⇒ k2 - 24 = 0
⇒ k2 = 24
`rArrk=sqrt24`
`rArrk=+-sqrt(4xx6)`
`rArrk=+-2sqrt6`
Hence, the value of `k=+-2sqrt6`
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