First, rearrange the given equation into the standard quadratic form Ax2+Bx+C=0. x+a+b=(
abx
ab+ax+bx
) Multiply both sides by ( ab+ax+bx ): ⇒(x+a+b)(ab+ax+bx)=abx ⇒x(ab)+x(ax)+x(bx)+a(ab)+a(ax)+a(bx)+b(ab)+b(ax)+b(bx)=abx ⇒abx+ax2+bx2+a2b+a2x+abx+ab2+abx+b2x=abx ⇒ax2+bx2+abx+a2x+abx+abx+b2x−abx+a2b+ab2=0 ⇒(a+b)x2+(a2x+b2x+2abx)+(a2b+ab2)=0 ⇒(a+b)x2+(a2+b2+2ab)x+ab(a+b)=0 Recognize that (a2+b2+2ab)=(a+b)2 : ⇒(a+b)x2+(a+b)2x+ab(a+b)=0 ⇒x2+(a+b)x+ab=0 Sum and product of the roots ( α and β ): Sum of roots: α+β=(−
