Tip:A–D to answerE for explanationV for videoS to reveal answer
LetPn=αn+βn,n∈N,ifP10=123,P9= 76, P8=47 and P1=1, then the quadratic equation having roots α1andβ1 is:
- A.
x2−x+1=0
- B.
x2+x−1=0
(Correct Answer) - C.
x2−x−1=0
Explanation
Pα′=α′′+β′′P10′=α10+β10=123P9′=α8+β9=47P1′=α+β=1P9+P8′=76+47=123α′3(α+1)+β′3(β+1)=123∴α′8(α+1)+β′8(β+1)=α10+β10α′2=α+1β′2=β+1
Given quadratic equation is,
x2=x+1
α+β=1,αβ=−1
α1+β1=αβα+β=−11
∴Quadratic equation is
x2−x(1)−1=0
x2+x−1=0
Explanation
Pα′=α′′+β′′P10′=α10+β10=123P9′=α8+β9=47P1′=α+β=1P9+P8′=76+47=123α′3(α+1)+β′3(β+1)=123∴α′8(α+1)+β′8(β+1)=α10+β10α′2=α+1β′2=β+1
Given quadratic equation is,
x2=x+1
α+β=1,αβ=−1
α1+β1=αβα+β=−11
∴Quadratic equation is
x2−x(1)−1=0
x2+x−1=0
