TS EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+4 x^2-9 x-36\) \(=0\) and \(\alpha < \beta < \gamma\) then \(\alpha+2 \beta+3 \gamma=\)
- A \(1\)
- B \(0\)
- C \(-1\)
- D \(-2\)
Answer & Solution
Correct Answer
(C) \(-1\)
Step-by-step Solution
Detailed explanation
\(x^3+4 x^2-9 x-36=0\) \(\Rightarrow \quad x^2(x+4)-9(x+4)=0\) \(\begin{aligned} & \Rightarrow \quad(x+4)(x+3)(x-3)=0 \\ & \therefore \quad x=-4,-3,3 \Rightarrow \alpha=-4, \beta=-3, \gamma=3 \\ & \Rightarrow \quad \alpha+2 \beta+3 \gamma=-4+2(-3)+3(3)=-1 .\end{aligned}\)
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