Answer to Question #20254 in Trigonometry for Kristen Woods

Question

solve each quadratic in form equation

4. (x-2)^2-3(x-2)+2=0

Answer 1

& (x-2)^2-3(x-2)+2=0

Let's find the discriminant of the given equation:

D = (-3)² - 4*1*2 = 9 - 8 = 1.

Now we can use the formula for the roots of a quadratic equation:

x-2 = ( -(-3) ± √D ) / (2*1) = ( 3 ± 1 ) / 2 = {2, 1}.

Therefore,

x1 - 2 = 2 ==> z1 = 4

and

x2 - 2 = 1 ==> x2 = 3.

So, this equation has two different solutions: {4, 3}.