A polynomial P(x) with leading coefficient 1 of degree 4 is such that P(alpha symbol) = 0 and its roots are 1, 2 and 3. Then, value of P(0) + p(4) is

Asked by vatsalchoudhary41 | 13th Dec, 2014, 06:30: AM

Expert Answer:

A space p o l y n o m i a l space P left parenthesis x right parenthesis space w i t h space l e a d i n g space c o e f f i c i e n t space o f space d e g r e e space 4 space i s P open parentheses x close parentheses equals x to the power of 4 plus b x cubed plus c x squared plus d x plus e equals 0 G i v e n space t h a t space r o o t s space o f space t h e space a b o v e space p o l y n o m i a l space a r e space 1 comma 2 space a n d space 3. T h u s comma space w e space h a v e comma P open parentheses 1 close parentheses equals 1 to the power of 4 plus b cross times 1 cubed plus c cross times 1 squared plus d cross times 1 plus e equals 0 rightwards double arrow 1 plus b plus c plus d plus e equals 0... left parenthesis 1 right parenthesis P open parentheses 2 close parentheses equals 2 to the power of 4 plus b cross times 2 cubed plus c cross times 2 squared plus d cross times 2 plus e equals 0 rightwards double arrow 16 plus 8 b plus 4 c plus 2 d plus e equals 0... left parenthesis 2 right parenthesis P open parentheses 3 close parentheses equals 3 to the power of 4 plus b cross times 3 cubed plus c cross times 3 squared plus d cross times 3 plus e equals 0 rightwards double arrow 81 plus 27 b plus 9 c plus 3 d plus e equals 0... left parenthesis 3 right parenthesis T h e r e space a r e space 3 space e q u a t i o n s space a n d space w e space n e e d space t o space f i n d space 4 space c o n s tan t s comma space w h i c h space i s space n o t space p o s s i b l e. P l e a s e space c h e c k space t h e space q u e s t i o n.

Answered by Vimala Ramamurthy | 15th Dec, 2014, 11:20: AM