Write an equation which has 1/5 as a root? Please explain with correct steps.
This was a question asked on 2012 final examination.
In my question bank, 35 x squared minus 2 x minus 1 equals 0 is the answer given.But I don't know how to do it.
 My exams are round the corner.Please hurry.....!!!!!!!!

Asked by Anishma Joseph | 11th Mar, 2015, 01:14: PM

Expert Answer:

H e r e comma space o n l y space r o o t space i s space g i v e n comma space t h a t space i s space x equals 1 fifth W e space c a n space c o n s i d e r space a n y space o t h e r space r o o t comma space s a y space x equals 2. space left parenthesis Y o u space c a n space c o n s i d e r space a n y space n u m b e r space a s space t h e r space o t h e r space r o o t right parenthesis S i n c e space x equals 1 fifth space a n d space x equals 2 comma space w e space h a v e comma space space open parentheses x minus 1 fifth close parentheses space a n d space open parentheses x minus 2 close parentheses space a r e space t h e space f a c t o r s space o f space t h e space r e q u i r e d space q u a d r a t i c space e q u a t i o n. T h u s comma space t h e space r e q u i r e d space q u a d r a t i c space e q u a t i o n space i s comma open parentheses x minus 1 fifth close parentheses open parentheses x minus 2 close parentheses equals 0 rightwards double arrow x squared minus 2 x minus x over 5 plus 2 over 5 equals 0 rightwards double arrow fraction numerator 5 x squared minus 10 x minus x plus 2 over denominator 5 end fraction equals 0 rightwards double arrow 5 x squared minus 11 x plus 2 equals 0 I n space y o u r space q u e s t i o n space b a n k space t h e y space h a v e space t a k e n space x equals negative 1 over 7 space a s space a n o t h e r space r o o t. T h u s comma space open parentheses x plus 1 over 7 close parentheses space a n d space open parentheses x minus 1 fifth close parentheses space a r e space t h e space f a c t o r s space o f space t h e space r e q u i r e d space q u a d r a t i c space e q u a t i o n. T h u s comma space t h e space r e q u i r e d space q u a d r a t i c space e q u a t i o n space i s comma open parentheses x minus 1 fifth close parentheses open parentheses x plus 1 over 7 close parentheses equals 0 rightwards double arrow x squared plus x over 7 minus x over 5 minus 1 over 35 equals 0 rightwards double arrow fraction numerator 35 x squared plus 5 x minus 7 x minus 1 over denominator 35 end fraction equals 0 rightwards double arrow 35 x squared minus 2 x minus 1 equals 0 T h u s comma space t h e space q u a d r a t i c space e q u a t i o n space h a v i n g space x equals 1 fifth space a s space o n e space o f space i t s space r o o t s space i s 35 x squared minus 2 x minus 1 equals 0

Answered by Vimala Ramamurthy | 12th Mar, 2015, 09:56: AM

Related Videos

Understand the concept of discriminant to classify roots of quadratic equat...

This video explains the concept of discriminant to classify roots of quadra...

This video explains the concept of discriminant to classify roots of quadra...

Nature of Roots

Quadratic Equations, Nature of Roots

This video covers an application on nature of roots

All Questions Ask Doubt