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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