How do you solve the equation #x^2-2x-1=0# by graphing?

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Answer 1 · 2016-12-20T17:17:51

Solutions are #-1/2# and #2 1/2#

When we draw graph of #y=x^2-2x-1#,

as a point on #x#-axis means #y=0#,

intercepts on #x#-axis, give the solution of equation #x^2-2x-1=0#

Now, if #x=2#, #y=-1#

if #x=0#, #y=-1#

if #x=-2#, #y=7#

if #x=1#, #y=-2#

if #x=3#, #y=2# and if #x=-3#, #y=14#

So joining points #{(2,-1),(0,-1),(-2,7),(1,-2),(3,2),(-3,14)}# we get the graph
graph{x^2-2x-1 [-10, 10, -5, 5]}

It shows that intercepts on #x#-axis are #-1/2# and #2 1/2#

Hence, these are the solutions.