AP EAMCET · Maths · Quadratic Equation
If the sum of any two roots of the equation \(x^3+p x^2+q x+r=0\) is zero, then
- A \(r=p q\)
- B \(p q^2=r\)
- C \(r^2=p q\)
- D \(p q r=1\)
Answer & Solution
Correct Answer
(A) \(r=p q\)
Step-by-step Solution
Detailed explanation
Given equation, \(x^3+p x^2+q x+r\) Let roots of given equation are \(\alpha, \beta\) and \(\gamma\) \(\alpha+\beta=0 ...(i)\) \(\alpha+\beta+\gamma=-p ...(ii)\) \(\alpha \beta+\beta \gamma+\gamma \alpha=+q ...(iii)\) and \(\alpha \beta \gamma=-r ...(iv)\) [From Eqs. (i) and…
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