# check work 3

• Feb 22nd 2009, 06:32 AM
william
check work 3
1. which of the following statements are true for f(x)=-2(x-1)(x-2)(x+3)

i) as x-> infinity, f(x)-> -infinity
ii) as x-> infinity, f(x)-> infinity
iii) as x-> -infinity, f(x)-> -infinity
iv) as x-> -infinity,f(x)-> infinity

a) i and iv
b) i and ii
c) i
d) i and iii

my choice: d)

2. which statement is true

a) a degree 4 function may have no real zero
b) a degree 4 function may have 1 or 2 real zeros
c) a degree 4 function may have 3 or 4 real zeros
d) all of the above

my choice: c)
• Feb 22nd 2009, 06:35 AM
Mush
Quote:

Originally Posted by william
1. which of the following statements are true for f(x)=-2(x-1)(x-2)(x+3)

i) as x-> infinity, f(x)-> -infinity
ii) as x-> infinity, f(x)-> infinity
iii) as x-> -infinity, f(x)-> -infinity
iv) as x-> -infinity,f(x)-> infinity

a) i and iv
b) i and ii
c) i
d) i and iii

my choice: d)

2. which statement is true

a) a degree 4 function may have no real zero
b) a degree 4 function may have 1 or 2 real zeros
c) a degree 4 function may have 3 or 4 real zeros
d) all of the above

my choice: c)

d would be true of the equation didn't have a minus sign in the beginning. But it does. So it's a.

All of the above are true for 2.
• Feb 22nd 2009, 06:44 AM
james_bond
Quote:

Originally Posted by william
1. which of the following statements are true for f(x)=-2(x-1)(x-2)(x+3)

i) as x-> infinity, f(x)-> -infinity
ii) as x-> infinity, f(x)-> infinity
iii) as x-> -infinity, f(x)-> -infinity
iv) as x-> -infinity,f(x)-> infinity

a) i and iv
b) i and ii
c) i
d) i and iii

my choice: d) <-WRONG the answer is a)

2. which statement is true

a) a degree 4 function may have no real zero
b) a degree 4 function may have 1 or 2 real zeros
c) a degree 4 function may have 3 or 4 real zeros
d) all of the above

my choice: c) <- WRONG I think they want answer d)

For Q2:
Any quartic can either have:

4 real roots -> quartic expressible in terms of a product of 4 linear factors

2 real roots -> quartic expressible in terms of a product of quadratic (with no real roots) and 2 linear factors

no real roots -> quartic expressible in terms of a product of 2 quadratic factors (with no real roots).