Methods2026 NHT Exam 2 Section A · Q11CAS active1 mark

Matching x-intercepts of a quadratic and a cubic

Let

$f : R \to R, f(x) = x^2 + cx + ab$ $g : R \to R, g(x) = (x - a)^2(x - b)$

where $a, b, c \in R$ .

Given that the graphs $y = f(x)$ and $y = g(x)$ have the same $x$ -intercepts, which one of the following must be true for all possible values of $a$ and $b$ ?

1 mark

c = ab

c = -ab

c = a + b

c = -(a + b)

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