What is the radical conjugate of 12−√5 ?
1 Answer
Jun 25, 2016
Explanation:
The conjugate of
This has the property that:
(12−√5)(12+√5)=122−(√5)2=144−5=139
Typical examples where you would use the conjugate would be:
- When rationalising the denominator of a quotient.
- When looking at zeros of a polynomial with rational (typically integer) coefficients.
For example:
2+3√512−√5
=(2+3√5)(12+√5)(12−√5)(12+√5)
=24+2√5+36√5+15144−5
=39+38√5139
The simplest polynomial with rational coefficients and zero
(x−(12−√5))(x−(12+√5))=x2−24x+139
