From Equation (I), we found that one root is x=0. To find other roots, we will solve Equation (II). Note that this is a quadratic equation. Thus, we will use the Quadratic Formula.
ax^2+bx+c=0 ⇔ x=- b±sqrt(b^2-4ac)/2a
To do so, we first need to identify a, b, and c.
x^2-6x+7=0
⇕
1x^2+( - 6)x+ 7=0
We see that a= 1, b= - 6, and c= 7. Let's substitute these values into the formula and simplify the right-hand side.
These roots of the quadratic equation are also roots of the given equation.
Roots
x=0, x=3+sqrt(2), x=3-sqrt(2)
We see that there are three roots. All three of them are real.
