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find a quadratic polynomial with zeroes 2root7and -2root7

Asked by tarjindersingh55 2nd October 2017, 11:59 AM
Answered by Expert
Answer:
begin mathsize 16px style Let space straight alpha equals 2 square root of 7 space and space straight beta equals negative 2 square root of 7
Now comma
sum space of space zeroes equals straight alpha plus straight beta equals 2 square root of 7 plus open parentheses negative 2 square root of 7 close parentheses equals 0
Product space of space zeroes equals αβ equals open parentheses 2 square root of 7 close parentheses open parentheses negative 2 square root of 7 close parentheses equals negative 28
Hence comma space the space required space quadratic space polynomial space is space given space by
straight f left parenthesis straight x right parenthesis equals straight k open curly brackets straight x squared minus open parentheses Sum space of space the space zeroes close parentheses straight x plus Product space of space the space zeroes comma space where space straight k space is space straight a space constant close curly brackets
rightwards double arrow straight f left parenthesis straight x right parenthesis equals straight k open parentheses straight x squared minus 0 straight x plus open parentheses negative 28 close parentheses close parentheses equals straight k open parentheses straight x squared minus 28 close parentheses comma space where space straight k space is space straight a space constant
end style
Answered by Expert 3rd October 2017, 8:54 AM
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