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AlgebraQ&A LibraryThe function f is given by f(x) = mx3+ nx2+ px + q, where m, n, p, q are integers.The graph of f passes through the point (0, 0).(a) Write down the value of q.The graph of f also passes through the point (3, 18).(b) Show that 27m+ 9n + 3p =18.The graph of f also passes through the points (1, 0) and (–1, –10).(c) Write down the other two linear equations in m, n, and p.(d) Find the function in standard form(e) The function f can also be written f (x) = x (x −1)(r x − s) where r and s areintegers. Find r and s.Question

Asked Nov 12, 2019

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The function f is given by f(x) = mx3

+ nx2

+ px + q, where m, n, p, q are integers.

The graph of f passes through the point (0, 0).

(a) Write down the value of q.

The graph of f also passes through the point (3, 18).

(b) Show that 27m+ 9n + 3p =18.

The graph of f also passes through the points (1, 0) and (–1, –10).

(c) Write down the other two linear equations in m, n, and p.

(d) Find the function in standard form

(e) The function f can also be written f (x) = x (x −1)(r x − s) where r and s are

integers. Find r and s.

Step 1

(a) the value of q.

Step 2

(b)

Step 3

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