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Algebra Level 5

x 2 + 3 a x + a + 1 = 0 \large x^2+3ax+a+1=0

Find the range of all values of a a for which exactly one root of the above equation lie between ( 0 , 1 ) (0,1) or ( 3 , 4 ) (3,4) .

( − 17 13 , − 1 ) ∪ ( − 1 , − 1 2 ) \left(-\frac{17}{13} , -1\right) \cup \left(-1,-\frac{1}{2}\right) None of the given choices ( − 17 13 , − 1 ) ∪ ( − 1 , − 1 2 ] \left(-\frac{17}{13} , -1\right) \cup \left(-1,-\frac{1}{2}\right] ( − 17 13 , − 1 2 ] \left(-\frac{17}{13} ,-\frac{1}{2}\right]

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Akshat Sharda by Akshat Sharda , 21, India

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