Question

If the equations x²+ax+b= 0 and x²+px+q= 0 have a common root then that root is

Answer 1

Step-by-step explanation:

${x}^{2} - ax + b = 0.....(1) \\ {x}^{2} + px + q = 0.....(2) \\ let \: \alpha \: be \: the \: common \: root \: then \: the \: roots \: of \: eq(ii) \: will \: be \: \alpha \: and \: \alpha .let \: \beta \: be \: the \: other \: root \: of \: eq \: (i) \: then \: root \: of \: equation \: (i) \: are \: \alpha \: and \: \beta \: and \: those \: of \: eq.(ii) \: are \: \alpha \: and \: \alpha \\ now \: \alpha + \beta = a \: ....(3) \\ \alpha \beta = b \: .....(4) \\ 2 \alpha = p....(5) \\ { \alpha }^{2} = q....(6) \\ b + q = \alpha \beta + {a}^{2} \\ = a( \alpha + \beta )$

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