    Question

# If the polynomial equation (x2+x+1)2−(m−3)(x2+x+1)+m=0,m∈R has two distinct real roots, then m lies in the interval

A
(454,)
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B
(,454)
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C
(92,)
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D
(9,)
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Solution

## The correct option is B (−∞,−454)(x2+x+1)2−(m−3)(x2+x+1)+m=0 Let t=x2+x+1=(x+12)2+34 ⇒t∈[34,∞) Given equation becomes t2−(m−3)t+m=0 ⋯(1) Let its roots be t1 and t2 (i) For every t>34, there exist two distinct real roots for x2+x+1=t (ii) For every t<34, there exists no real roots for x2+x+1=t Given equation will have two distinct roots iff for equation (1), roots are of form t1<34 and t2>34 i.e., 34 lies in between the roots of equation (1). ⇒f(34)<0 ⇒916−(m−3)34+m<0 ⇒m<−454  Suggest Corrections  0      Similar questions  Related Videos   Preparing Alkanes
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