Question

What shape do degree 3 functions have?

Answer 1

Answer: Third degree polynomials are also known as cubic polynomials. Cubics have these characteristics: One to three roots. Two or zero extrema.

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Answer 2

Let ()
p
(
x
)
be a polynomial of degree 3
3
with real coefficients. Which of the following is possible ?

a) ()
p
(
x
)
has no real roots

b) ()
p
(
x
)
has exactly two real roots

c) (1)=−1,(2)=1,(3)=11,(4)=35
p
(
1
)
=
−
1
,
p
(
2
)
=
1
,
p
(
3
)
=
11
,
p
(
4
)
=
35

d) −1
i
−
1
and +1
i
+
1
are roots of ()
p
(
x
)
, where =−1‾‾‾√