The region where x² - 4x + 3 < 0 is: A. x < 1 and x < 3
The graph of y = x² - 4x + 3 is a parabola that opens upwards. To find the values for which x² - 4x + 3 < 0, we need to consider the points where the parabola intersects the x-axis, which are the solutions to the equation y = 0.
Factoring the quadratic equation, we get:
(x - 3)(x - 1) = 0
From this, we find the solutions for x:
x = 1 and x = 3
Now, we can plug these values of x into the original equation to find the corresponding values of y:
y = (1)² - 4(1) + 3 = 0
y = (3)² - 4(3) + 3 = 0
However, we are only interested in the values of x for which y < 0, as this represents the region where x² - 4x + 3 < 0. From the previous equation, we can see that y = 0 when x = 1 and x = 3. Therefore, the region where x² - 4x + 3 < 0 is: A. x < 1 and x < 3
Complete question:
The graph of y = x² - 4x + 3 is shown. Select the values for which x² - 4x + 3 < 0.
A. x<1 and x<3
B. x<1 and x>3
C. x>1 and x<3
D. x>1 and x>3