using the following equation for parts a, b and c: 0 = x^2 - 4x + 3.

a) how many roots and what type of roots does this equation have? find the discriminant and use it to answer this question.

b) solve using the quadratic formula. (show all steps of work)

c) substitute each solution back into the equation and show that the solutions are correct! (show all steps of work)

(will try an give brainliest, if i can figure it out bc i'm still new to this app : d)

First rewrite the formula by moving all the terms to the left side:

-x^2 + 4x - 3 = 0

A) Find the discriminant using the formula b^2 -4(ac)

where a  is the term in front of  x^2, which is -1 ( -x is can also be written as -1x)

b = 4 and c = 3

Now you have 4^2 - 4(-1-3) = 16 - 12 = 4

The discriminant is 4.

Because the discriminant is greater than 0, there are 2 real roots.

B) -x^2 + 4x - 3 = 0

Using the quadratic formula -b+/- SQRT(b^2-4(ac)  / 2a

Replace the letters with their values like in Part A:

-4 +/- SQRT(4^2-4*(-1*-3) = 2 * -1

x = 2 +1 = 3 ans x = 2-1 = 1

X = 3, 1

C)

1^2 - 4(1) +3 = 1-4 +3 = 0 TRUE

3^2 - 4(3) +3 = 9 -12 +3 = 0 TRUE