solve x^2+ 2x= -2 by graphing and indicate the roots.?

Question

a. between -3 and -2 and between 0 and 1
b. between -1 and 0 and between 2 and 3
c. no real solutions
d. -1, 1

Answer 1

The way to graph it is to put it in parabola form.

x² + 2x = -2

y = x² + 2x + 2

y = x² + 2x + 1 + 1

y = (x + 1)² + 1

This is parabola form:

y = a(x - h)² + k, where (h, k) is the vertex

So, the vertex of this equation is (-1, 1), and since the coefficient of x² is positive, it opens upward.

Which means it never crosses the x-axis.

Which means there are no real solutions, choice c.