Grades 11-12 Video Solutions 2024-2024_11-12

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Video Summary

The function \( f \) has exactly two roots, subject to the relationship \( f(20-x) = f(22+x) \). Suppose one root is \( a \), then \( f(a) = 0 \). Choosing \( x = 20-a \), we find \( f(42-a) = 0 \) as well. This implies the roots are \( a \) and \( 42-a \). The sum of the roots is \( a + (42-a) = 42 \). Any other configuration implies more than two roots, contradicting the problem's constraints. Thus, the sum of the roots is 42.

Keywords

function roots

symmetry

root sum

two roots

mathematical relationship