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CBSE Class 10 Answered

One zero of the polynomial 3x square +16x square +15x_18 is 2/3 find the other zero of the polynomial 
Asked by Princesteve331 | 24 Aug, 2018, 06:27: PM
answered-by-expert Expert Answer
begin mathsize 16px style Given colon space straight p left parenthesis straight x right parenthesis space equals space 3 straight x cubed space plus space 16 straight x squared space plus space 15 straight x space minus space 18 space and space 2 over 3 space is space straight a space factor space of space straight p left parenthesis straight x right parenthesis.
Since comma space straight x space equals space 2 over 3 space is space straight a space zero space of space straight p left parenthesis straight x right parenthesis space
rightwards double arrow space open parentheses straight x space minus space 2 over 3 close parentheses space is space straight a space factor space of space straight p left parenthesis straight x right parenthesis.
Now comma space by space long space division space method space we space will space find space out space the space other space factor space of space straight p left parenthesis straight x right parenthesis. end style
begin mathsize 16px style straight p left parenthesis straight x right parenthesis space equals space 3 straight x cubed space plus space 16 straight x squared space plus space 15 straight x space minus space 18
space space space space space space space equals open parentheses straight x space minus space 2 over 3 close parentheses open parentheses 3 straight x squared space space plus space 18 straight x space plus space 27 close parentheses
space space space space space space space equals open parentheses straight x space minus space 2 over 3 close parentheses open parentheses 3 straight x squared space space plus space 9 straight x space plus 9 straight x space plus space 27 close parentheses
space space space space space space space equals open parentheses straight x space minus space 2 over 3 close parentheses open parentheses 3 straight x space plus space 9 close parentheses open parentheses straight x space plus space 3 close parentheses
rightwards double arrow zeroes space of space straight p left parenthesis straight x right parenthesis space are space as space follows
open parentheses straight x space minus space 2 over 3 close parentheses open parentheses 3 straight x space plus space 9 close parentheses open parentheses straight x space plus space 3 close parentheses space equals space 0
rightwards double arrow straight x space equals space 2 over 3 comma space minus 3 comma space minus 3
Therefore space the space two space remaining space zeroes space are space minus 3 comma space minus 3.
end style
Answered by Yasmeen Khan | 24 Aug, 2018, 07:26: PM
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