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<div>Write an equation which has 1/5 as a root? Please explain with correct steps.</div> <div>This was a question asked on 2012 final examination.</div> <div>In my question bank, <img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=00a4eda7a3548533029ceadc1cb63605.png" alt="35 x squared minus 2 x minus 1 equals 0" align="middle" /> is the answer given.But I don't know how to do it.</div> <div> My exams are round the corner.Please hurry.....!!!!!!!!</div>

Asked by Anishma Joseph | 11 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 | 12 Mar, 2015, 09:56: AM

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