TMUA 2021 · Paper 1 · Question 8

The line $y = 2 x + 3$ meets the curve $y = x^{2} + b x + c$ at exactly one point.

The line $y = 4 x - 2$ also meets the curve $y = x^{2} + b x + c$ at exactly one point.

What is the value of $b - c$ ?

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