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What is the largest value of k such that the quadratic x^2 - 5x + k + x^2 - 11x + 3 has at least one real root?

 Jul 5, 2022
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Simplify to \(2x^2 - 16x + 3 + k\).

 

The quadratic has exactly 1 solution when the discriminant(\(b^2 - 4ac\)) is 0. 


This means we have the equation: \(256 - 4 \times 2 \times (3 + k) = 0\)

 

Solving, we find \(k = \color{brown}\boxed{29}\)

 Jul 5, 2022

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