Question

Find the slope of the line segment joining points (0,1) and where the polynomial p(x)=x2-2x+1 touches the x-axis

Answer 1

Required slope = - 1

Step-by-step explanation:

The given polynomial is

p(x) = x² - 2x + 1

In order to find the intersection of p(x) and the x-axis we put y = 0, i.e., p(x) = 0

Now, p(x) = 0 gives

x² - 2x + 1 = 0

or, (x - 1)² = 0

or, x - 1 = 0

i.e., x = 1

So the polynomial p(x) touches the x-axis at (1, 0)

We have the points (0, 1) and (1, 0)

Thus the slope of the line segment joining the points (0, 1) and (1, 0) be

(0 - 1)/(1 - 0) = - 1/1 = - 1