# How do you find the roots, real and imaginary, of y= x^2 - 3x + 4-(x-1)^2  using the quadratic formula?

Mar 25, 2016

The root is: $x = 3$

#### Explanation:

Observe here you have two binomial so the recipe is
a) Expand the 2nd binomial
b) simplify the combined binomial and get the resultant
c) Find roots using

Let's apply the recipe:
a) Expand: ${\left(x - 1\right)}^{2} \implies {x}^{2} - 2 x + 1$
b) Simplify: $y = {\cancel{x}}^{2} - 3 x + 4 - \left({\cancel{x}}^{2} - 2 x + 1\right) = - x + 3$
c) Find root: $x = 3$

Remark : You said using quadratic formula, notice you did not need it here, because the polynomial was reduced to 1st order via simplification