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Q.

The rational roots of the cubic equation x3 + 14 kx2 + 56kx – 64k3 = 0 are in the ratio 1 : 2 : 4. Find the possible value of K


Class:                9


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a

0 only

b

1 only

c

2, 0

d

None of the above 

answer is D.

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Detailed Solution

Given, roots of the given equation are in the ratio 1:2:4
Let's consider 1a, 2a, 4a as roots
Sum of roots
⇒ 7a = –14k
⇒ a = –2k
Product of roots
⇒ 8a3 = 64k3
⇒ a3 = 8k3
⇒ (–2k)3 = 8k3 … (Substituting a = –2k)
⇒ –8k3 = 8k3
⇒ 8k3 + 8k3 = 0
⇒ 16k3 = 0
⇒ k3 = 0
⇒ k = 0
⇒ a = –2k
⇒ a = –2 × 0.
⇒ a = 0
The ratio of cubic equation is 1 : 2 : 4
Therefore, option 4 is the correct answer
  
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