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 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.

 

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Expert Answer

Step 1

(a) the value of q.

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f(x)= mx +nx +px + q (a) The graph of f passes through the point (0,0) The value of q 0 =mo3 n0+ p0 + q or, q 0

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Step 2

(b)

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(b) The graph of f also passes through the point (3, 18) m33 n32 p3 q = 18 or, 27 m + 9n + Зр+0 %3D18 27m + 9n+ 3р%3D18 or

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Step 3
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(c) The graph off also passes through the points (1,0) and (-1.-10). The other two linear equations in m, n, and p. Point (1,0) m13 n12pl +q = 0 т+n+ p+0%3D0 т +n+ p%3 0 or Point 1 10) m(-1)n(-p-1)+q= 0 3 — т +п- р+ 0%3D0 or — т +п- р%3D0 or

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