Let β ∈ R and let f : R → R be given by f ( x ) = x 7 − 7 x + β , then Match each entry in List-I to the correct entry in List-II List - I List - II (P) f ( x ) = 0 has three distinct real roots if (1

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Let β ∈ R and let f : R → R be given by f ( x ) = x 7 − 7 x + β , then Match each entry in List-I to the correct entry in List-II List - I List - II (P) f ( x ) = 0 has three distinct real roots if (1) β > 6 (Q) f ( x ) = 0 has exactly two distinct real roots if (2) − 6 < β < 6 (R) f ( x ) = 0 has only one real root if (3) β = e − 1 (S) If f ( 2 ) = 0 , then (4) β = { − 6 , 6 } (5) β = − 114 The correct option is

TestHub · Accepted Answer

f ( x ) = x 7 − 7 x + β = 0 ∴ β = 7 x − x 7 ∴ f ( x ) = 0 has three distinct real roots if β ∈ ( − 6 , 6 ) f ( x ) = 0 has exactly two distinct real roots if β = { − 6 , 6 } f ( x ) = 0 has only one real root if β ∈ ( − ∞ , − 6 ) ∪ ( 6 , ∞ ) f ( 2 ) = 114 + β = 0 ∴ β = − 114

List - I	List - II
(P) $f (x) = 0$ has three distinct real roots if	(1) $β > 6$
(Q) $f (x) = 0$ has exactly two distinct real roots if	(2) $- 6 < β < 6$
(R) $f (x) = 0$ has only one real root if	(3) $β = e^{- 1}$
(S) If $f (2) = 0$ , then	(4) $β = {- 6, 6}$
	(5) $β = - 114$

Mathematics - Application of Derivative Question with Solution | TestHub

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JEE Advanced (2028)