Offer a geometric explanation to why the equation x²-6x+10=0 has no real solutions.

Answered.

Step-by-step explanation:

let the equation be

y = x^2-6x+10

y = x^2-6x+9+1

(y-1) = (x-3) ^2

comparing it with standard equation of a parabola

y=4x^2, clearly both will be facing upward

has vertex (0,0) where as the parabola (y-1) = (x-3) ^2 has vertex as (3,1)

clearly it will not cut the x - axis and hence it will not have any real roots.

moreover, Mathematically x²-6x+10=0 on solving has roots 3-i and 3+i