ax2 + bx + c

Asked by VINOD G. KHETAN | 6th Jun, 2014, 11:49: AM

Expert Answer:

I n space o r d e r space t o space g e t space r e a l space r o o t s space f o r space q u a d r a t i c space e q u a t i o n comma space t h e space v a l u e space b squared minus 4 a c space greater or equal than space 0  s o space l e t s space f i n d space o u t space w h a t space a r e space t h e space p o s s i b l e space c o m b i n a t i o n s space a v a i l a b l e space t o space g e t space r e a l space r o o t s space left parenthesis a comma space b comma space c right parenthesis  I f space b space equals space 1 comma space t h e n space t h e r e space i s space n o space p o s s i b i l t y space a t space a l l space f o r space r e a l space r o o t s. space S o space Z e r o  I f space b space equals space 2 comma space t h e n space a equals space 1 space a n d space c space equals space 1 space i s space t h e space o n l y space p o s s i b i l t y space left parenthesis 1 comma space 2 comma space 1 right parenthesis. space S o space 1 space f o r space t h i s space c a s e  I f space b space equals space 3 comma space t h e n space p o s s i b l e space s e t s space a r e space left parenthesis 1 comma space 3 comma space 1 right parenthesis space left parenthesis 1 comma space 3 comma space 2 right parenthesis space left parenthesis 2 comma space 3 comma space 1 right parenthesis. space S o space 3 space f o r space t h i s space c a s e  I f space b space equals 4 comma space t h e n space p o s s i b l e space s e t s space a r e space left parenthesis 1 space 4 space 1 right parenthesis space left parenthesis 1 space 4 space 2 right parenthesis space left parenthesis 2 space 4 space 1 right parenthesis space left parenthesis 1 space 4 space 3 right parenthesis space left parenthesis 3 space 4 space 1 right parenthesis space left parenthesis 2 space 4 space 2 right parenthesis. space S o space 6 space f o r space t h i s space c a s e  I f space b space equals space 5 comma space t h e n space p o s s i b l e space s e t s space a r e space space left parenthesis 1 space 5 space 1 right parenthesis space left parenthesis 1 space 5 space 2 right parenthesis space left parenthesis 2 space 5 space 1 right parenthesis space left parenthesis 1 space 5 space 3 right parenthesis space left parenthesis 3 space 5 space 1 right parenthesis space left parenthesis 2 space 5 space 2 right parenthesis space left parenthesis 3 space 5 space 2 right parenthesis space left parenthesis 2 space 5 space 3 space right parenthesis. space S o space 8 space f o r space t h i s space c a s e  I f space b space equals space 6 comma space t h e n space p o s s i b e space s e t s space a r e space left parenthesis 1 space 6 space 1 right parenthesis space left parenthesis 1 space 6 space 2 right parenthesis space left parenthesis 2 space 6 space 1 right parenthesis space left parenthesis 1 space 6 space 3 right parenthesis space left parenthesis 3 space 6 space 1 right parenthesis space left parenthesis 2 space 6 space 2 right parenthesis space left parenthesis 3 space 6 space 2 right parenthesis space left parenthesis 2 space 6 space 3 space right parenthesis space left parenthesis 3 space 6 space 3 right parenthesis. space S o space 9 space f o r space t h i s space c a s e  T o t a l space p o s s i b i l i t e s space f o r space r e a l space r o o t s space a r e space 0 space plus thin space 1 space plus space 3 plus space 6 space plus space 8 space plus space 9 space equals space 27  S o space p r o b a b i l i t y space i s space 27 over 216 equals 1 over 8

Answered by Dharma Teja | 6th Jun, 2014, 07:13: PM

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