If one root of the equation 2x2 + 3x – k = 0 is 6, what is the value of k?
The question should say that k is a constant. In that case, if 6 is a 'root' of the equation, that just means that x=6 is one solution to the equation. So we can plug in x=6:
2x^2 + 3x - k &= 0 \\
2(6^2) + (3)(6) - k &= 0 \\
72 + 18 &= k \\
90 &= k
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