obtain all the zeroes of p(x)=2x4+7x3-19x2-14x+30 if two zeroes are root 2 and -root 2

 

Asked by PRAMOD122497 | 15th Jun, 2019, 04:13: PM

Expert Answer:

L e t space a space a n d space b space b e space t h e space t w o space o t h e r space z e r o e s space o f space p left parenthesis x right parenthesis equals 2 x to the power of 4 plus 7 x cubed minus 19 x squared minus 14 x plus 30
rightwards double arrow 2 plus left parenthesis negative 2 right parenthesis plus a plus b equals negative 7 over 2 space space a n d space 2 left parenthesis negative 2 right parenthesis a b equals 30 over 2
a plus b equals negative 7 over 2 space... space left parenthesis i right parenthesis space a n d space a b equals negative 15 space... space left parenthesis i i right parenthesis
U sin g space left parenthesis i right parenthesis space i n space left parenthesis i i right parenthesis comma space w e space h a v e
a open parentheses negative 7 over 2 minus a close parentheses equals negative 15
a squared plus 7 over 2 a minus 15 equals 0
2 a squared plus 7 a minus 30 equals 0
2 a squared plus 12 a minus 5 a minus 30 equals 0
2 a left parenthesis a plus 6 right parenthesis minus 5 left parenthesis a plus 6 right parenthesis equals 0
left parenthesis 2 a minus 5 right parenthesis left parenthesis a plus 6 right parenthesis equals 0
a equals 5 over 2 space o r space a equals negative 6
H e n c e comma space t h e space o t h e r space t w o space z e r o e s space a r e space 5 over 2 space a n d space minus 6.

Answered by Renu Varma | 16th Jun, 2019, 12:21: AM

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