Q.

If the absolute value of the difference of the roots of the equation x2+ax+1=0 exceeds 3a, then

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a

a∈(−∞,−1)∪(4,∞)

b

a∈(4,∞)

c

a∈(−1,4)

d

a∈[0,4)

answer is A.

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Detailed Solution

We have, |α−β|>3a⇒|α−β|2>3a⇒(α+β)2−4αβ>3a⇒a2−4>3a⇒a2−3a−4>0⇒(a−4)(a+1)>0⇒a∈(−∞,−1)∪(4,∞)
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If the absolute value of the difference of the roots of the equation x2+ax+1=0 exceeds 3a, then