Question

If one root of quadratic equations x^2+ax+b and x2+bx+a=0 is common find relationship between a and b

Answer 1

the given equations are

${x}^{2} + ax + b = 0 \: \: \: \: \: \: \: ...(1) \\ {x}^{2} + bx + a = 0 \: \: \: \: \: \: \: ...(2)$

$on \: doing \: (1) - (2) \: we \: get \\ (a - b)x = (a - b) \\ x = 1 \\ therefore \: x = 1 \: is \: \: common \: root \: of \: the \: equations \\ so \: on \: putting \: x = 1 \:in \: (1) \: we \: get \\ {(1)}^{2} + a(1) + b = 0 \\ a + b = - 1$