THE DIFFERENCE OF TWO ZEROES OF POLYNOMIAL IS 1 AND PRODUCT IS 12 FIND SUM OF TWO ZEROES
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Let the two zeroes be alpha and beta
therefore alpha - beta =1
Squaring on both sides,
(alpha-beta)^2=(1)^2
alpha ^2 -2 *alpha*beta+ beta^2=1
(alpha)^2+(beta)^2-2(12)=1.
[since alpha*beta=12]
alpha^2+beta^2=1+24=25
[alpha^2+beta^2=(alpha+beta)^2-2*alpha*beta]
(alpha+beta)^2-2(12)=25
(alpha+beta)^2=25+24
(alpha+beta)^2=49
alpha+beta=√49
alpha+beta=7
Therefore sum of two zeroes=7
therefore alpha - beta =1
Squaring on both sides,
(alpha-beta)^2=(1)^2
alpha ^2 -2 *alpha*beta+ beta^2=1
(alpha)^2+(beta)^2-2(12)=1.
[since alpha*beta=12]
alpha^2+beta^2=1+24=25
[alpha^2+beta^2=(alpha+beta)^2-2*alpha*beta]
(alpha+beta)^2-2(12)=25
(alpha+beta)^2=25+24
(alpha+beta)^2=49
alpha+beta=√49
alpha+beta=7
Therefore sum of two zeroes=7
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