Find the zeroes of the polynomial f(x)=ax2-(a2+1)x+a, and verify the relationship between the zeroes and the coefficients. Share with your friends Share 5 Lovina Kansal answered this Dear student We havef(x)=ax2-a2+1x+aWe will find the zeros of the given polynomial by discriminant methodx=a2+1±a2+12-4a22ax=a2+1±a4+1+2a2-4a22ax=a2+1±a4+1-2a22ax=a2+1±a2-12ax=a2+1+a2-12a and x=a2+1-a2-12ax=a and x=1aThus, the zeros of f(x) are α=a and β=1aNow, -Coefficient of xCoefficient of x2=--a2+1a=a2+1aand Contant termCoefficient of x2=aa=1Also, α+β=a+1a=a2+1a and αβ=a×1a=1Hence,α+β=-Coefficient of xCoefficient of x2and, αβ=Contant termCoefficient of x2 Regards -4 View Full Answer
