JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(\alpha=1\) and \(\beta=1+i\sqrt{2}\), where \(i=\sqrt{-1}\) are two roots of the equation \(x^3+ax^2+bx+c=0\), \(a,b,c \in \mathbb{R}\), then \(\int_{-1}^{1}(x^3+ax^2+bx+c)dx\) is equal to:
- A \(-2\)
- B \(-4\)
- C \(-8\)
- D \(-10\)
Answer & Solution
Correct Answer
(C) \(-8\)
Step-by-step Solution
Detailed explanation
Since \(a, b, c \in \mathbb{R}\), the complex roots of the equation \(x^3+ax^2+bx+c=0\) must occur in conjugate pairs. Given roots are \(\alpha = 1\) and \(\beta = 1+i\sqrt{2}\). The third root must be \(\gamma = 1-i\sqrt{2}\). The polynomial is given by:…
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