find the con

Asked by mdkingofficial786 | 21st Dec, 2020, 04:37: PM

Expert Answer:

Question: Find the condition such that difference of the roots of the equation ax2 + bx + c = 0 is equal to the product of the roots.
Solution:
Let space straight alpha space and space straight beta space be space the space two space roots space of space the space equation.
As space per space the space question comma space we space have
straight alpha minus straight beta equals αβ
rightwards double arrow square root of open parentheses straight alpha minus straight beta close parentheses squared end root equals αβ
rightwards double arrow square root of open parentheses straight alpha plus straight beta close parentheses squared minus 4 αβ end root equals αβ
As space straight alpha plus straight beta space equals space minus straight b over straight a space space and space space αβ equals straight c over straight a comma space we space get
square root of straight b squared over straight a squared minus 4 straight c over straight a end root equals straight c over straight a
rightwards double arrow space square root of straight b squared over straight a squared minus fraction numerator 4 ac over denominator straight a squared end fraction end root equals straight c over straight a
rightwards double arrow fraction numerator square root of straight b squared minus 4 ac end root over denominator straight a end fraction equals straight c over straight a
rightwards double arrow straight c equals square root of straight b squared minus 4 ac end root

Answered by Renu Varma | 22nd Dec, 2020, 11:09: AM