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if alpha and beta are the zeros of the polynomial f(x)=x^2-3x-2. find a quadratic polynomial whose zeroes are 1/2alpha +beta,1/2beta +alpha

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see first find roots from given quadratic polynomial , x²-3x+2=0=x²-x-2x+2=0=x(x-1)-2(x-1)=0(x-1)(x-2)=0x=1 or ,x=2 given zeroes of quadratic polynomial 1/2alpha+beta ,1/2beta+alpha substitute=1/2(1)+2, 1/2(2)+1=1/4,1/5formula is x²-(alpha+beta)x+alpha*beta =0therefore x²-(1/4+1/5)x+1/4*1/5=0=ans is 20x^2 - 9x +1 =0

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if alpha and beta are the zeros of the polynomial f(x)=x^2-3x-2. find a quadratic polynomial whose zeroes are 1/2alpha +beta,1/2beta +alpha
X^2-9x/2+3/2

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see first find roots from given quadratic polynomial , x²-3x+2=0=x²-x-2x+2=0=x(x-1)-2(x-1)=0(x-1)(x-2)=0x=1 or ,x=2 given zeroes of quadratic polynomial 1/2alpha+beta ,1/2beta+alpha substitute=1/2(1)+2, 1/2(2)+1=1/4,1/5formula is x²-(alpha+beta)x+alpha*beta =0therefore x²-(1/4+1/5)x+1/4*1/5=0=ans is 20x^2 - 9x +1 =0