WBJEE · Maths · Sequences and Series
Consider a quadratic equation \(a x^2+2 b x+c=0\) where \(a, b, c\) are positive real numbers. If the equation has no real root, then which of the following is true?
- A a, b, c cannot be in A.P. or H.P. but can be in G.P.
- B a, b, c cannot be in G.P. or H.P. but can be in A.P.
- C \(a, b, c\) cannot be in A.P. or G.P. but can be in H.P.
- D a, b, c cannot be in A.P., G.P. or H.P.
Answer & Solution
Correct Answer
(C) \(a, b, c\) cannot be in A.P. or G.P. but can be in H.P.
Step-by-step Solution
Detailed explanation
Hint : For no real root \(\begin{aligned} & (2 b)^2-4 a c 0 \end{aligned}\) If in \(A P\), then \(a+c=2 b\) i.e., \(\mathrm{x}=-1\) a solution \(\begin{aligned} & \therefore a, b, c \text { not in AP } \\ & \because b^2 < a c \end{aligned}\) \(\therefore a, b, c\) not in GP For…
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