JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\alpha, \beta, \gamma\) be the three roots of the equation \(x ^3+ bx + c =0\). If \(\beta \gamma=1=-\alpha\), then \(b^3+2 c^3-3 \alpha^3-6 \beta^3-8 \gamma^3\) is equal to \(......\).
- A \(21\)
- B \(\frac{169}{8}\)
- C \(19\)
- D \(\frac{155}{8}\)
Answer & Solution
Correct Answer
(C) \(19\)
Step-by-step Solution
Detailed explanation
\(\beta \gamma=1\) \(\alpha=-1\) \(\text { Put } \alpha=-1\) \(-1-b+c=0\) \(c-b=1\) \(\text { also }\) \(\alpha \cdot \beta \cdot \gamma=-c\) \(-1=-c \Rightarrow c=1\) \(\therefore b=0\) \(x^3+1=0\) \(\alpha=-1, \beta=- w , \gamma=- w ^2\)…
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