# *finding zero of order 4 polynominial

• MHB
• karush
In summary, the conversation is about finding the zeros of the function $f(x)=16x^4+3x^2-2$. The quadratic formula is used to solve for the zeros, but there is a discrepancy between the solutions obtained by setting $u=x^2$ and the ones provided by W|A. The difference lies in the coefficient of the 4th degree term, which should be divided by 2 before applying the quadratic formula. Therefore, the correct solutions are $x=\pm\frac{1}{4}\sqrt{-\frac{3}{2}+\frac{\sqrt{137}}{2}}$.
karush
Gold Member
MHB
Find the zeros
$$f(x)=16x^4+3x^2-2$$
ok I presume we can solve this with the quadratic formula even with powers of 4 and 2
by setting $u=x^2$ I was able to get$$x=\pm\sqrt{-\frac{3}{2}+\frac{\sqrt{137}}{2}}$$but $W\vert A$ says the answer is$$x=\pm\frac{1}{4}\sqrt{-\frac{3}{2}+\frac{\sqrt{137}}{2}}$$where does the $\frac{1}{4}$ come from?

$$\tiny{140.56}$$

You should get (when applying the quadratic formula and discarding the complex roots):

$$\displaystyle x=\pm\sqrt{-\frac{3}{32}+\frac{\sqrt{137}}{32}}$$

The 32 comes from twice the coefficient of the 4th degree term. And this is equivalent to W|A's result.

Start by dividing by 2: 8x^4 + (3/2)x^2 - 1 = 0

Wilmer said:
Start by dividing by 2: 8x^4 + (3/2)x^2 - 1 = 0

\begin{align}\displaystyle
y&=8x^4 + (3/2)x^2 - 1 \\
&=\frac{-(3/2)\pm\sqrt{(3/2)^2-4(8)(-1)}}{2(8)}\\
&=\frac{1}{16} \left(-\frac{3}{2} \pm \frac{\sqrt{137}}{2}\right)
\end{align}

maybe

The square root of that changes the 1/16 to 1/4

## 1. What does "finding zero of order 4 polynomial" mean?

"Finding zero of order 4 polynomial" refers to the process of determining the values of the variable that make a polynomial equation of fourth degree equal to zero.

## 2. How do you find the zero of order 4 polynomial?

To find the zero of order 4 polynomial, you can use methods such as factoring, the rational root theorem, or the quadratic formula. These methods allow you to solve the polynomial equation and determine the values of the variable that make it equal to zero.

## 3. Why is finding the zero of order 4 polynomial important?

Finding the zero of order 4 polynomial is important because it helps in solving real-world problems in various fields such as engineering, physics, and economics. It also allows for the analysis and understanding of complex polynomial functions.

## 4. What are the possible number of zeros for a polynomial of order 4?

A polynomial of order 4 can have up to four complex zeros. However, it is not always the case that all four zeros will be distinct or real. The number of zeros can also be less than four depending on the nature of the polynomial equation.

## 5. Can a polynomial of order 4 have no real zeros?

Yes, a polynomial of order 4 can have no real zeros. This means that all four zeros are complex numbers. However, it is also possible for a polynomial of order 4 to have both real and complex zeros.

• General Math
Replies
19
Views
2K
• General Math
Replies
2
Views
1K
• General Math
Replies
5
Views
1K
• General Math
Replies
3
Views
754
• General Math
Replies
2
Views
932
• General Math
Replies
4
Views
944
• General Math
Replies
7
Views
1K
• General Math
Replies
2
Views
902
• General Math
Replies
2
Views
1K
• General Math
Replies
2
Views
1K