TS EAMCET · Maths · Quadratic Equation
The condition that the roots of \(x^3-b x^2+c x-d=0\) are in geometric progression is
- A \(c^3=b^3 d\)
- B \(c^2=b^2 d\)
- C \(c=b d^3\)
- D \(c=b d^2\)
Answer & Solution
Correct Answer
(A) \(c^3=b^3 d\)
Step-by-step Solution
Detailed explanation
Equation, \(x^3-b x^2+c x-d=0\) Let the roots of this cubic equation in GP are \(\left(\frac{a}{r}, a, a r\right)\) Then, Sum of the roots \(\frac{a}{r}+a+a r=-\left(\frac{-b}{1}\right) \Rightarrow b\) \(\Rightarrow \quad a\left(\frac{1}{r}+1+r\right)=b\) \(\ldots\) (i) and…
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