Let $x_1, x_2, \ldots, x_6$ be the roots of the polynomial equation $x^6+2 x^5+4 x^4+8 x^3+16 x^2+32 x+64=0$. Then,
Let $x_1, x_2, \ldots, x_6$ be the roots of the polynomial equation $x^6+2 x^5+4 x^4+8 x^3+16 x^2+32 x+64=0$. Then,
- [KVPY 2017]
- A
$\left|x_i\right|=2$ for exactly one value of $i$
- B
$\left|x_i\right|=2$ for exactly two values of $i$
- C
$\left|x_i\right|=2$ for all values of $i$
- D
$\left|x_i\right|=2$ for no value of $i$
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- [KVPY 2020]
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Consider the equation $(1+a+b)^2=3\left(1+a^2+b^{2})\right.$ where $a, b$ are real numbers. Then,
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- [KVPY 2016]