The quadratic equation, who's roots are reciprocal of the roots of the equation- ax^2+bx+c,is?

Asked by drhimasingh | 26th May, 2020, 11:31: PM

Expert Answer:

Let alpha and beta be the roots of the quadratic equation ax2+bx+c=0
Using space the space relation space between space the space roots space and space coefficients comma space we space have
straight alpha plus straight beta equals negative straight b over straight a space and space αβ equals straight c over straight a
1 over straight alpha plus 1 over straight beta equals fraction numerator straight alpha plus straight beta over denominator αβ end fraction equals fraction numerator negative begin display style straight b over straight a end style over denominator begin display style straight c over straight a end style end fraction equals negative straight b over straight c
1 over straight alpha 1 over straight beta equals 1 over αβ equals fraction numerator 1 over denominator begin display style straight c over straight a end style end fraction equals straight a over straight c
The space required space quadratic space equation space is space straight x squared plus open parentheses 1 over straight alpha plus 1 over straight beta close parentheses straight x plus open parentheses 1 over straight alpha 1 over straight beta close parentheses equals 0
rightwards double arrow straight x squared minus straight b over straight c straight x plus straight a over straight c equals 0
rightwards double arrow cx squared minus bx plus straight a equals 0

Answered by Renu Varma | 27th May, 2020, 11:50: AM