Let f : R → R be the function f(x) = (x – a1)(x–a2)+(x–a2)(x�

1.	Let f : R → R be the function f(x) = (x – a1)(x–a2)+(x–a2)(x–a3) + (x– a3) (x–a1) with a1, a2, a3 ∈ R. Then f(x) > 0 if and only if – (A) At least two of a1, a2, a3 are equal (B) a1 = a2 = a3 (C) a1, a2, a3 are all distinct (D) a1, a2, a3 , are all positive and distinct
Answer» Correct :- (B) a₁= a₂ = a₃ Explanation :- Only when a₁ = a₂ = a₃ In other cases f(x) will take both positive and negative values

Let f : R → R be the function f(x) = (x – a1)(x–a2)+(x–a2)(x–a3) + (x– a3) (x–a1) with a1, a2, a3 ∈ R. Then f(x) > 0 if and only if – (A) At least two of a1, a2, a3 are equal (B) a1 = a2 = a3 (C) a1, a2, a3 are all distinct (D) a1, a2, a3 , are all positive and distinct

Answer»

Correct :- (B) a₁= a₂ = a₃

Explanation :-

Only when a₁ = a₂ = a₃ In other cases f(x) will take both positive and negative values

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Let f : R → R be the function f(x) = (x – a1)(x–a2)+(x–a2)(x–a3) + (x– a3) (x–a1) with a1, a2, a3 ∈ R. Then f(x) &gt; 0 if and only if – (A) At least two of a1, a2, a3 are equal (B) a1 = a2 = a3 (C) a1, a2, a3 are all distinct (D) a1, a2, a3 , are all positive and distinct

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Let f : R → R be the function f(x) = (x – a1)(x–a2)+(x–a2)(x–a3) + (x– a3) (x–a1) with a1, a2, a3 ∈ R. Then f(x) > 0 if and only if – (A) At least two of a1, a2, a3 are equal (B) a1 = a2 = a3 (C) a1, a2, a3 are all distinct (D) a1, a2, a3 , are all positive and distinct