# Thread: zeros and square root

1. ## zeros and square root

1. I was asked how many zeros need to exist in order for the following functions to exist.

a) linear
c) cubic
d) quartic
e) quintic

My answer would be none, but can anyone tell me if i am right?

2. Also, for a equation such as 2Cos(x)-√3 = 0
do i only take the positive root when solving for x or do i take the positve and negative?
and how about for 2Cos(x)+√3 = 0

2. Originally Posted by imthatgirl
...

2. Also, for a equation such as 2Cos(x)-√3 = 0
do i only take the positive root when solving for x or do i take the positve and negative?
and how about for 2Cos(x)+√3 = 0
Hi,

$2\cos(x)-\sqrt{3}=0~\iff~\cos(x)=\frac12 \sqrt{3}$..... $~\implies~x=\frac16 \cdot \pi+2n \cdot \pi~\vee~x=-\frac16 \cdot \pi+2n \cdot \pi ,\ n \in \mathbb{Z}$

$2\cos(x)+\sqrt{3}=0~\iff~\cos(x)=-\frac12 \sqrt{3}$..... $~\implies~x=\frac56 \cdot \pi+2n \cdot \pi~\vee~x=-\frac56 \cdot \pi+2n \cdot \pi\ ,\ n \in \mathbb{Z}$

3. Originally Posted by imthatgirl
1. I was asked how many zeros need to exist in order for the following functions to exist.

a) linear Mr F says: No zeros needed for existence. Eg. The horizontal line y = 3.

b) quadratic Mr F says: No zeros needed for existence. Eg. $y = x^2 + 1$.

c) cubic Mr F says: At least one zero needed for existence. All cubics approach +oo and -oo => must cut x-axis at least once.

d) quartic Mr F says: No zeros needed for existence. Eg. $y = x^4 + 1$.

e) quintic Mr F says: At least one zero needed for existence. Same argument as cubic.

My answer would be none, but can anyone tell me if i am right? Mr F says: No. See above.
[snip]
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