TS EAMCET · Maths · Quadratic Equation
Given that the roots of \(x^3+3 p x^2+3 q x+r=0\) are in harmonic progression. Then,
- A \(2 q^3=r(3 p q-r)\)
- B \(q^3=r(3 p q-r)\)
- C \(q^3=-r(3 p q-r)\)
- D \(q^3=r(r+3 p q)\)
Answer & Solution
Correct Answer
(A) \(2 q^3=r(3 p q-r)\)
Step-by-step Solution
Detailed explanation
\(x^3+3 p x^2+3 q x+r=0\) roots are in HP. So, let roots are \([2,3,6]\) that is in \(\mathrm{HP}\). So, \(x^3-\) (sum of root) \(x^2+\) (sum of product of two-two roots \(] x\) - Product of roots \(=0\)…
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