AP EAMCET · Maths · Quadratic Equation
If the roots of \(x^3-p x^2+q x-r=0\) are in AP. Then,
- A \(2 p^3-9 p q+27 r=0\)
- B \(2 p^3+9 p q-27 r=0\)
- C \(2 p^3-8 p q+27 r=0\)
- D \(2 p^3-9 p q+28 r=0\)
Answer & Solution
Correct Answer
(A) \(2 p^3-9 p q+27 r=0\)
Step-by-step Solution
Detailed explanation
Let \(a-d, a, a+d\) are roots of \[ x^3-p x^2+q x-r=0 \] Sum of roots \(=-\frac{b}{a}\) \[ \begin{aligned} a-d+a+a+d & =-\frac{(-p)}{1} \\ 3 a & =p \\ a & =\frac{p}{3} \end{aligned} \] Since, \(a=\frac{P}{3}\) should be satisfied by given equation. So, put \(x=\frac{p}{3}\) in…
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