A

9000064505

Level: 
A
Find the factorization of the following quadratic polynomial in the set of polynomial with complex valued coefficients. \[ 2x^{2} + 32 \]
\(2(x + 4\mathrm{i})(x - 4\mathrm{i})\)
\(2(x - 4\mathrm{i})^{2}\)
\((x + 4\mathrm{i})(x - 4\mathrm{i})\)
\(2(x + 4\mathrm{i})^{2}\)

9000064508

Level: 
A
Solve the following quadratic equation in the complex plane. \[ 2x^{2} + x + 1 = 0 \]
\(x_{1, 2} = \frac{-1\pm \mathrm{i}\sqrt{7}} {4} \)
\(x_{1, 2} = \frac{-1\pm \mathrm{i}\sqrt{7}} {2} \)
\(x_{1, 2} = \frac{1\pm \mathrm{i}\sqrt{7}} {4} \)
\(x_{1, 2} = \frac{1\pm \mathrm{i}\sqrt{7}} {2} \)

9000065301

Level: 
A
Find the recurrence equations for the arithmetic sequence with the first term \(a_{1} = 4\) and the common difference \(d = -2\).
\(a_{1} = 4;\ a_{n+1} = a_{n} - 2,\ n\in\mathbb{N}\)
\(a_{1} = 4;\ a_{n+1} = a_{1} - 2,\ n\in\mathbb{N}\)
\(a_{n} = 4 + a_{n+2},\ n\in\mathbb{N}\)
\(a_{n+1} = a_{n} + 2,\ n\in\mathbb{N}\)

9000065608

Level: 
A
Using integrals write formula for the area of the shaded region.
\(\int _{a}^{b}(f(x) - g(x))\, \mathrm{d}x +\int _{ b}^{c}(g(x) - f(x))\, \mathrm{d}x\)
\(\int _{a}^{b}(g(x) - f(x))\, \mathrm{d}x +\int _{ b}^{c}(g(x) - f(x))\, \mathrm{d}x\)
\(\int _{a}^{b}(f(x) - g(x))\, \mathrm{d}x +\int _{ b}^{c}(f(x) - g(x))\, \mathrm{d}x\)
\(\int _{a}^{b}(f(x) + g(x))\, \mathrm{d}x +\int _{ b}^{c}(f(x) - g(x))\, \mathrm{d}x\)