Use a quadratic discriminant to identify successful parameter values and calculate their probability.

Use a quadratic discriminant to identify successful parameter values and calculate their probability.

6 marks

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A family of functions is given by \(f(x)=x^2+3x+k\), where \(k\in\{1,2,3,4,5,6,7\}\). One of these functions is chosen at random.[6]

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Answer:Among \(\{1,2,3,4,5,6,7\}\), only \(k=1,2\) work, so the probability is \(\frac27\).

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