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CBSE Class 10 Answered

Let alpha and beta are the zeroes of a quadratic polynomial 2x²-5x-6 then form a quadratic polynomial whose zeroes are alpha+beta and alpha×beta
Asked by geetayadav18081983 | 15 Jun, 2022, 01:19: PM
Expert Answer
Given quadratic equation is
 
f(x) = 2x2 -5x - 6
 
roots of above quadratic equation are  begin mathsize 14px style fraction numerator 5 plus square root of 25 minus 4 left parenthesis 2 right parenthesis left parenthesis negative 6 right parenthesis end root over denominator 2 cross times 2 end fraction end style and begin mathsize 14px style fraction numerator 5 minus square root of 25 minus 4 left parenthesis 2 right parenthesis left parenthesis negative 6 right parenthesis end root over denominator 2 cross times 2 end fraction end style
roots of above quadratic equation are  begin mathsize 14px style fraction numerator 5 plus square root of 73 over denominator 4 end fraction end style and begin mathsize 14px style fraction numerator 5 minus square root of 73 over denominator 4 end fraction end style
Hence begin mathsize 14px style alpha space equals space fraction numerator 5 plus square root of 73 over denominator 4 end fraction end style and begin mathsize 14px style beta space equals space fraction numerator 5 minus square root of 73 over denominator 4 end fraction end style
If roots of a quadratic equition are (α + β ) and ( α β ) , then quadratic equation is
 
g(x) = x2 - (α + β + α β ) x + (α + β ) ( α β )
 
begin mathsize 14px style alpha space plus beta equals space fraction numerator 5 plus square root of 73 over denominator 4 end fraction plus fraction numerator 5 minus square root of 73 over denominator 4 end fraction space equals space 5 over 2 end style
begin mathsize 14px style alpha space beta space equals space open parentheses space fraction numerator 5 plus square root of 73 over denominator 4 end fraction space close parentheses space space stretchy left parenthesis space fraction numerator 5 minus square root of 73 over denominator 4 end fraction space stretchy right parenthesis space equals space 1 over 16 open parentheses 25 plus 73 minus 10 square root of 73 close parentheses space equals 49 over 8 minus 5 over 8 square root of 73 end style
Hence quadratic equation is
 
begin mathsize 14px style g left parenthesis x right parenthesis space equals space x squared space minus space open parentheses 5 over 2 space plus space 49 over 8 space minus space 5 over 8 square root of 73 close parentheses x space plus 5 over 16 open parentheses 49 minus 5 square root of 73 close parentheses end style
begin mathsize 14px style g left parenthesis x right parenthesis space equals space x squared space minus space open parentheses space 69 over 8 space minus space 5 over 8 square root of 73 close parentheses x space plus 5 over 16 open parentheses 49 minus 5 square root of 73 close parentheses end style
 
begin mathsize 14px style g left parenthesis x right parenthesis space equals space 16 space x squared space minus space open parentheses space 138 space minus space 10 square root of 73 close parentheses x space plus open parentheses 245 minus 25 square root of 73 close parentheses end style
Answered by Thiyagarajan K | 15 Jun, 2022, 02:43: PM

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