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CBSE Class 10 Answered

If alpha is a zero of the polynomial p(x)=3x^4 - 5x^3 + 7x^2 -5x + 3 then show that 1/alpha is also a zero of it 
Asked by DIY | 09 Oct, 2019, 07:49: PM
answered-by-expert Expert Answer
alpha space i s space a space z e r o space o f space t h e space p o l y n o m i a l space p left parenthesis x right parenthesis equals 3 x to the power of 4 minus 5 x cubed plus 7 x squared minus 5 x plus 3 rightwards double arrow 3 alpha to the power of 4 minus 5 alpha cubed plus 7 alpha squared minus 5 alpha plus 3 equals 0 space... space left parenthesis i right parenthesis N o w comma space c o n s i d e r 3 open parentheses 1 over alpha close parentheses to the power of 4 minus 5 open parentheses 1 over alpha close parentheses cubed plus 7 open parentheses 1 over alpha close parentheses squared minus 5 open parentheses 1 over alpha close parentheses plus 3 equals 3 cross times 1 over alpha to the power of 4 minus 5 cross times 1 over alpha cubed plus 7 cross times 1 over alpha squared minus 5 cross times 1 over alpha plus 3 equals 1 over alpha to the power of 4 open parentheses 3 minus 5 alpha plus 7 alpha squared minus 5 alpha cubed plus 3 alpha to the power of 4 close parentheses equals 1 over alpha to the power of 4 open parentheses 3 alpha to the power of 4 minus 5 alpha cubed plus 7 alpha squared minus 5 alpha plus 3 close parentheses equals 1 over alpha to the power of 4 open parentheses 0 close parentheses space.... space F r o m space left parenthesis i right parenthesis equals 0 H e n c e comma space 1 over alpha space i s space a l s o space a space z e r o space o f space t h e space p o l y n o m i a l space p left parenthesis x right parenthesis.
Answered by Renu Varma | 11 Oct, 2019, 09:36: AM

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