If alpha and beta are the zeroes of the polynomial 2x2-5x+5 then find the polynomial whose zeroes are 2alpha+3beta and 3alpha +2beta
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Alpha +beta=-(coefficient of x)/coefficient of x^2
A+B = 5/2
AB = coefficient of x/coefficient of x^2
AB=5/2
New zeroes are (3A+2B),(2A+3B)
3A+2B+3B+2A=5A+5B=5(A+B)=5×5/2=25/2
On multiplying new zeroes we get,
6A^2+6B^2 +13AB = 6(A^2+B^2)+13AB= 6(15/2)+13×5/2=135/2........{(A+B)^2 = A^2+B^2 +2AB , here A^2+B^2 = 15/2}
New polynomial will be 2x^2-25x +135
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