WBJEE · Maths · Quadratic Equation
If \(a, b, c\) are in A.P. and if the equations \((b-c) x^2+(c-a) x+(a-b)=0\) and \(2(c+a) x^2+(b+c) x=0\) have a common root, then
- A \(a^2, b^2, c^2\) are in A.P.
- B \(a^2, c^2, b^2\) are in A.P.
- C \(c^2, a^2, b^2\) are in A.P.
- D \(a^2, b^2, c^2\) are in G.P.
Answer & Solution
Correct Answer
(B) \(a^2, c^2, b^2\) are in A.P.
Step-by-step Solution
Detailed explanation
Given: - \(a, b, c\) are in A.P. \(\Rightarrow b=\frac{a+c}{2}\) - Two quadratic equations have a common root: \(\begin{array}{l} (b-c) x^2+(c-a) x+(a-b)=0 ... (1) \\ 2(c+a) x^2+(b+c) x=0 ... (2) \end{array}\) Step-by-step approach: Let the common root be \(\alpha\). Then it…
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