For what values of m does the graph of y is equal to m x squared minus 5 x minus 2 have no x -intercepts?

An x-intercept occurs where y = 0, so solve mx² − 5x − 2 = 0. For a quadratic to have no real solutions, its discriminant must be negative: (−5)² − 4(m)(−2) = 25 + 8m < 0, which gives m < −25/8. Therefore, the correct choice is “m is less than negative 25 eighths.”

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