document.write( "Question 37501: Find a polynomial of degree 4 with intger coefifients that has 2 square root + 5 square root as a root. \n" ); document.write( "

Algebra.Com's Answer #25681 by venugopalramana(3286) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find a polynomial of degree 4 with intger coefifients that has 2 square root + 5 square root as a root.
\n" ); document.write( "FIRST LET US PUT A QUADRATIC WITH (2^0.5+5^0.5) AND -(2^0.5+5^0.5) AS ROOTS WE GET THE QUADRATIC AS
\n" ); document.write( "{X+(2^0.5+5^0.5)}{X-(2^0.5+5^0.5)}=0
\n" ); document.write( "=X^2-(2^0.5+5^0.5)^2=X^2-2-5-2*(10^0.5)=(X^2-7)-2*(10^0.5)=0
\n" ); document.write( "NOW LET US MULTIPLY WITH THE CONJUGATE AGAIN
\n" ); document.write( "{(X^2-7)-2*(10^0.5)}{(X^2-7)+2*(10^0.5)}=0
\n" ); document.write( "=(X^2-7)^2-4*10=0
\n" ); document.write( "X^4-14X^2+49-40=0
\n" ); document.write( "X^4-14X^2+9=0 \n" ); document.write( "

\n" );