AP EAMCET · Maths · Quadratic Equation
If the roots of the equation \(x^3-a x^2+b x-c=0\) are in HP, then the mean of the roots is
- A \(\frac{a}{3 c}\)
- B \(\frac{b}{3 c}\)
- C a
- D \(\frac{3 c}{b}\)
Answer & Solution
Correct Answer
(D) \(\frac{3 c}{b}\)
Step-by-step Solution
Detailed explanation
Let \(\alpha, \beta, \gamma\) are roots of equation \[ \begin{array}{r} x^3-a x^2+b x-c=0 \\ \alpha+\beta+\gamma=a \\ \alpha \beta+\beta \gamma+\gamma \alpha=b \\ \alpha \beta \gamma=c \end{array} \] It is given that \(\alpha, \beta, \gamma\) are in HP.…
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