Question

if a and b are two zeroes of polynomial f(x)= x^2 - x - 3 , find a polynomial whose zeroes are 2a+1 and 2b +1, find the polynomial

Answer 1

x²-x-3=0
using sridharacharya's rule,

x=(-B+-√(B²-4AC))/2A
where A=1,B=-1,C=-3

x=(-(-1)+-√((-1)²-4(1)(-3)))/2(1)
x=(1+-√(1+12))/2
x=(1+-√13)/2
x=(1+√13)/2 or x=(1-√13)/2

let a=(1+√13)/2 , b=(1-√13)/2
the equation is
f(x)=(x-(2a+1))(x-(2b+1))
f(x)=(x-(2((1+√13)/2)+1)(x-(2((1-√13)/2)+1)
f(x)=(x-(2+√13))(x-(2-√13))
f(x)=x²-(2-√13)x+(2+√13)x+(2²-(√13)²)
f(x)=x²-2x+x√13+2x+√13x+(4-13)
f(x)=x²+2√13x-9