in the polynomial p(x)=x^2+ax+b,p(3+root2)=0 p(3-root2)=0,write this polynomial after finding a and b please answer fast - Maths - Mathematics of Chance

Question

in the polynomial p(x)=x^2+ax+b,p(3+root2)=0 p(3-root2)=0,write
this polynomial after finding a and b please answer fast

Neha Sethi · Accepted Answer

Dear student
Given: px=x2+ax+bWe have, p3+2=0⇒3+22+a3+2+b=0⇒9+2+62+3a+2a+b=0⇒11+62+3a+2a+b=0  
1Also, we havep3-2=0⇒3-22+a3-2+b=0⇒9+2-62+3a-2a+b=0⇒11-62+3a-2a+b=0 
2Adding 1 and 2, we get22+6a+2b=011+3a+b=0b=-11+3aPutting in 1, we get⇒11+62+3a+2a-11-3a=0⇒62+2a=0⇒2a=-62⇒a=-6So, b=-11+3-6=-11-18=7So, px=x2+ax+b=x2-6x+7
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in the polynomial p(x)=x^2+ax+b,p(3+root2)=0 p(3-root2)=0,write this polynomial after finding a and b.please answer fast