We appreciate your visit to Solve tex 8x 3 48x 2 5x 30 0 tex tex x tex Fill in the blank. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve the polynomial equation [tex]\(8x^3 + 48x^2 - 5x - 30 = 0\)[/tex], we can follow these steps:
1. Identify Possible Rational Roots: We can use the Rational Root Theorem, which suggests that any rational root of the polynomial is a factor of the constant term (-30) divided by the leading coefficient (8). This gives us possible rational roots, but this step often requires checking several options.
2. Synthetic Division or Factoring: Sometimes, identifying at least one rational root can help factor the polynomial, but in this case, solving directly is more efficient using the roots already identified.
3. Find The Roots: The equation has the following solutions:
- [tex]\( x = -6 \)[/tex]
- [tex]\( x = -\frac{\sqrt{10}}{4} \)[/tex]
- [tex]\( x = \frac{\sqrt{10}}{4} \)[/tex]
These roots can be quadratic, real, or involve square roots, as seen here with the presence of [tex]\(\sqrt{10}\)[/tex].
Therefore, the solutions to the equation [tex]\(8x^3 + 48x^2 - 5x - 30 = 0\)[/tex] are [tex]\( x = -6 \)[/tex], [tex]\( x = -\frac{\sqrt{10}}{4} \)[/tex], and [tex]\( x = \frac{\sqrt{10}}{4} \)[/tex].
1. Identify Possible Rational Roots: We can use the Rational Root Theorem, which suggests that any rational root of the polynomial is a factor of the constant term (-30) divided by the leading coefficient (8). This gives us possible rational roots, but this step often requires checking several options.
2. Synthetic Division or Factoring: Sometimes, identifying at least one rational root can help factor the polynomial, but in this case, solving directly is more efficient using the roots already identified.
3. Find The Roots: The equation has the following solutions:
- [tex]\( x = -6 \)[/tex]
- [tex]\( x = -\frac{\sqrt{10}}{4} \)[/tex]
- [tex]\( x = \frac{\sqrt{10}}{4} \)[/tex]
These roots can be quadratic, real, or involve square roots, as seen here with the presence of [tex]\(\sqrt{10}\)[/tex].
Therefore, the solutions to the equation [tex]\(8x^3 + 48x^2 - 5x - 30 = 0\)[/tex] are [tex]\( x = -6 \)[/tex], [tex]\( x = -\frac{\sqrt{10}}{4} \)[/tex], and [tex]\( x = \frac{\sqrt{10}}{4} \)[/tex].
Thanks for taking the time to read Solve tex 8x 3 48x 2 5x 30 0 tex tex x tex Fill in the blank. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
