TS EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, 2 \beta\) are the real roots of the equation \(x^3-9 x^2+k=0\) and \(k \in \mathbb{R}-\{0\}\), then \(14 \beta=\)
- A 28
- B 36
- C 18
- D 54
Answer & Solution
Correct Answer
(D) 54
Step-by-step Solution
Detailed explanation
Given equation \({x}^3-9 {x}^2+{k}=0\) where \({k} \in {R}-\{0\}\). Here, \(\alpha, \beta \& 2 \beta\) are roots. \(\alpha+\beta+2 \beta=-(-9)=9\) ...(i) \(\begin{aligned} & \alpha \beta+\beta(2 \beta)+2 \beta(\alpha)=0 \\ & \alpha \beta+2 \beta^2+2 \beta \alpha=0\end{aligned}\)…
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