1. ## 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)

2. 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.

3. 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).