[ Investigation of a quadratic trinomial ]

A quadratic trinomial $y=a x^{2}+b x+c$ has no roots and $a+b+c>0$. Determine the sign of the coefficient $c$.

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![](https://cdn.mathpix.com/cropped/2024_05_06_a1c7cb3d3682c5b3cf5fg-32.jpg?height=212&width=180&top_left_y=440&top_left_x=939)

The quadratic polynomial has no roots, which means its graph does not intersect the x-axis. Since \( y(1) = a + b + c > 0 \), the graph is located in the upper half-plane (see the figure), therefore, \( c = y(0) > 0 \).

## Answer

\( c > 0 \).