If #x^2-6x+5=0# and #x^2-12x+p=0# have a common root, what is #p#?

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Answer 1 · 2017-07-23T08:24:01

#p=11# or #35#.

As #x^2-6x+5=0# can be writen as

#(x-1)(x-5)=0#

its roots are #1#and #5#.

Let the roots of #x^2-12x+p=0# be #alpha# and #beta# of which #alpha# is common root.

then as #alpha+beta=12# and #alphabeta=p#,

if #alpha=5#, then #beta=7# and #p=5xx7=35#

and if #alpha=1#, then #beta=11# and #p=11#.