Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
The roots of the given polynomials exist [tex]$x=8+\sqrt{10}$[/tex], and [tex]$x=8-\sqrt{10}$[/tex].
What is the formula of the quadratic equation?
For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are
[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]
Therefore by using the formula we have
[tex]$x^{2}-16 x+54=0$[/tex]
Let, a = 1, b = -16 and c = 54
Substitute the values in the above equation, and we get
[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$[/tex]
simplifying the equation, we get
[tex]${data-answer}amp;x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1} \\[/tex]
[tex]${data-answer}amp;x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1} \\[/tex]
[tex]${data-answer}amp;x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]
Therefore, the roots of the given polynomials are [tex]$x=8+\sqrt{10}$[/tex], and
[tex]$x=8-\sqrt{10}$[/tex].
To learn more about quadratic equations refer to:
brainly.com/question/1214333
#SPJ4
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.