What is the degree of a polynomial that has roots of , , , and ?
Options
A
8
B
3
C
7
D
1
Answer & Analysis
Answer
C
Analysis
According to the properties:
1. For a polynomial with real coefficients, if a root is of the form , then is also a root.
2. According to the Conjugate Root Theorem, if a polynomial has real coefficients and a complex number is a root, then its complex conjugate is also a root.
Here one of the roots is , so is also a root. Also, one of the roots is , so its conjugate
Want More Practice Questions?
Access thousands of practice questions with detailed explanations on Scholardog.
'%3e%3cpath%20fill-rule='evenodd'%20clip-rule='evenodd'%20d='M1.75736%201.75736C0%203.51472%200%206.34315%200%2012C0%2017.6569%200%2020.4853%201.75736%2022.2426C3.51472%2024%206.34315%2024%2012%2024C17.6569%2024%2020.4853%2024%2022.2426%2022.2426C24%2020.4853%2024%2017.6569%2024%2012C24%206.34315%2024%203.51472%2022.2426%201.75736C20.4853%200%2017.6569%200%2012%200C6.34315%200%203.51472%200%201.75736%201.75736ZM18.1727%206H16.026L12.4879%209.8345L9.42953%206H5L10.2925%2012.5633L5.27636%2018H7.42427L11.2963%2013.8054L14.6798%2018H19L13.4829%2011.0834L18.1727%206ZM16.4622%2016.7816H15.2724L7.50688%207.15475H8.78349L16.4622%2016.7816Z'%20fill='%23535A74'/%3e%3c/g%3e%3cdefs%3e%3cclipPath%20id='clip0_774_453'%3e%3crect%20width='24'%20height='24'%20fill='white'/%3e%3c/clipPath%3e%3c/defs%3e%3c/svg%3e){kind=small}
'%3e%3crect%20id='大小'%20width='24'%20height='24'%20transform='translate(510%20188)'%20fill='%23fff'%20opacity='0'/%3e%3cpath%20id='路径_1057'%20data-name='路径%201057'%20d='M14,2a12,12,0,0,0-1.875,23.854V17.469H9.079V14h3.047V11.356c0-3.007,1.791-4.669,4.533-4.669a18.454,18.454,0,0,1,2.686.234V9.875H17.832a1.734,1.734,0,0,0-1.956,1.874V14H19.2l-.532,3.469h-2.8v8.385A12,12,0,0,0,14,2Z'%20transform='translate(507.999%20186)'%20fill='%23535a74'/%3e%3c/g%3e%3c/svg%3e){kind=small}
'%3e%3cpath%20fill-rule='evenodd'%20clip-rule='evenodd'%20d='M0%2012C0%2017.6569%200%2020.4853%201.75736%2022.2426C3.51472%2024%206.34315%2024%2012%2024C17.6569%2024%2020.4853%2024%2022.2426%2022.2426C24%2020.4853%2024%2017.6569%2024%2012C24%206.34315%2024%203.51472%2022.2426%201.75736C20.4853%200%2017.6569%200%2012%200C6.34315%200%203.51472%200%201.75736%201.75736C0%203.51472%200%206.34315%200%2012ZM4.96484%209.49609V19.043H7.93359V9.49609H4.96484ZM4.72656%206.47656C4.72656%207.42578%205.49609%208.19531%206.44922%208.19531C7.39844%208.19531%208.16797%207.42188%208.16797%206.47656C8.16797%205.52734%207.39844%204.75781%206.44922%204.75781C5.49609%204.75781%204.72656%205.52734%204.72656%206.47656ZM16.0781%2019.043H19.043V13.8047C19.043%2011.2344%2018.4883%209.25781%2015.4844%209.25781C14.043%209.25781%2013.0742%2010.0508%2012.6797%2010.8008H12.6406V9.49609H9.79688V19.043H12.7578V14.3242C12.7578%2013.0781%2012.9922%2011.8711%2014.5352%2011.8711C16.0586%2011.8711%2016.0781%2013.2969%2016.0781%2014.4023V19.043Z'%20fill='%23535A74'/%3e%3c/g%3e%3cdefs%3e%3cclipPath%20id='clip0_774_461'%3e%3crect%20width='24'%20height='24'%20fill='white'/%3e%3c/clipPath%3e%3c/defs%3e%3c/svg%3e){kind=small}
'%3e%3cpath%20fill-rule='evenodd'%20clip-rule='evenodd'%20d='M0%2012C0%206.34315%200%203.51472%201.75736%201.75736C3.51472%200%206.34315%200%2012%200C17.6569%200%2020.4853%200%2022.2426%201.75736C24%203.51472%2024%206.34315%2024%2012C24%2017.6569%2024%2020.4853%2022.2426%2022.2426C20.4853%2024%2017.6569%2024%2012%2024C6.34315%2024%203.51472%2024%201.75736%2022.2426C0%2020.4853%200%2017.6569%200%2012ZM12%205.83594C8.59688%205.83594%205.83594%208.59688%205.83594%2012C5.83594%2015.4031%208.59688%2018.1641%2012%2018.1641C15.4031%2018.1641%2018.1641%2015.4031%2018.1641%2012C18.1641%208.59688%2015.4031%205.83594%2012%205.83594ZM12%2015.9984C9.79219%2015.9984%208.00156%2014.2078%208.00156%2012C8.00156%209.79219%209.79219%208.00156%2012%208.00156C14.2078%208.00156%2015.9984%209.79219%2015.9984%2012C15.9984%2014.2078%2014.2078%2015.9984%2012%2015.9984ZM18.4078%207.0312C19.2%207.0312%2019.8469%206.38902%2019.8469%205.59214C19.8469%204.79995%2019.2%204.15308%2018.4078%204.15308C17.6156%204.15308%2016.9688%204.79526%2016.9688%205.59214C16.9688%206.38433%2017.6109%207.0312%2018.4078%207.0312Z'%20fill='%23535A74'/%3e%3c/g%3e%3cdefs%3e%3cclipPath%20id='clip0_774_455'%3e%3crect%20width='24'%20height='24'%20fill='white'/%3e%3c/clipPath%3e%3c/defs%3e%3c/svg%3e){kind=small}