The degree of the polynomial function f(x) is 4. The roots of the equation f(x)=0 are −2, −1, 1 and 3. Which graph could be the graph of f(x)?
Mathematics
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Question
The degree of the polynomial function f(x) is 4.
The roots of the equation f(x)=0 are −2, −1, 1 and 3.
Which graph could be the graph of f(x)?
The roots of the equation f(x)=0 are −2, −1, 1 and 3.
Which graph could be the graph of f(x)?
1 Answer

1. User Answers eudora
Answer:
Option A
Stepbystep explanation:
Degree of the polynomial function = 4
That means highest degree term of the given polynomial has power = 4
If the roots of a quadratic polynomial are a, b, c, d then the polynomial function will be,
f(x) = (x  a)(x  b)(x  c)(x  d)
It's given in the question that roots are x = 2, 1, 1 and 3
Therefore, polynomial function will be,
f(x) = (x + 2)(x + 1)(x  1)(x  3)
From the given options, graph A shows that the graph intersects the xaxis at x = 2, 1, 1 and 3
Therefore, Option A will be the answer.