AP EAMCET · Maths · Quadratic Equation
The condition that the roots of \(x^3-b x^2+c x-d=0\) are in arithmetic progression is
- A \(9 c b=2 b^3+27 d\)
- B \(9 c b=2 d^3+27 b\)
- C \(9 c d=2 d^3+27 b\)
- D \(9 c d=2 b^3+27 d\)
Answer & Solution
Correct Answer
(A) \(9 c b=2 b^3+27 d\)
Step-by-step Solution
Detailed explanation
Let roots in A.P. be as \(\alpha-r, \alpha, \alpha+r\) Sum of roots \(=b\) \(\Rightarrow \alpha-r+\alpha+\alpha+r=b \Rightarrow \alpha=\frac{b}{3}\) \(\alpha\) is root of \(x^3-b x^2+c x-d=0\)…
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