B2. Calculate the sum of the zeros of the polynomial $p(x)=4 x^{3}-8 x^{2}+x+3$.






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B2. The first root $x_{1}=1$ can be guessed and verified using Horner's algorithm. The quotient of the given polynomial and the linear polynomial $x-1$ is a polynomial of the second degree, the roots of which can be calculated using the formula for finding the roots of a quadratic function. The sought roots are $x_{1}=1, x_{2}=\frac{3}{2}$, and $x_{3}=-\frac{1}{2}$, and the sum of the roots is $x_{1}+x_{2}+x_{3}=2$.

![](https://cdn.mathpix.com/cropped/2024_06_07_bce9c6e2a6f4f88bb0deg-15.jpg?height=46&width=1619&top_left_y=2350&top_left_x=287)

Calculated first root..................................................................................................................

Quadratic equation whose solutions are the further roots ..............................................................................

Calculated roots .....................................................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_bce9c6e2a6f4f88bb0deg-15.jpg?height=49&width=1625&top_left_y=2551&top_left_x=290)

NOTE: The roots are $x_{1}=1, x_{2}=\frac{3}{2}, x_{3}=-\frac{1}{2}$.