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  1. For what value of k, the equation x2 + 2(k - 4) x + 2k = 0 has equal roots ?
    1. 6 and 4
    2. 8 and 2
    3. 10 and 4
    4. 12 and 2
    5. None of the above
Correct Option: B

Given equation is
x2 + 2(k - 4)x + 2k = 0
On comparing with ax2 + bx + c = 0
Here, a = 1, b = 2(k -4), c = 2k
Since, the root are equal, we have D = 0.
b2 - 4ac = 0
∴ 4(k - 4)2 - 8k = 0
4(k2 + 16 - 8k) - 8k = 0
⇒ 4k2 + 64 - 32k - 8k = 0
⇒ 4k2 - 40k + 64 = 0
⇒ k2 - 10k + 16 = 0
⇒ k2 - 8k - 2k + 16 = 0
⇒ k(k - 8) -2 (k - 8) = 0
⇒ (k - 8) (k - 2) = 0
Hence, the value of k 8 or 2.



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