What are the x-intercepts of the graph of the function f(x) = x² + 5x - 36?

Solution:

The equation x² + 5x - 36 represents a parabola. To find its x-intercepts the equation needs to be factorized by splitting the middle terms.

f(x) = x² + 9x - 4x - 36

= x(x + 9) - 4(x + 9)

= (x + 9)(x - 4)

x intercepts are obtained by putting y = 0

Therefore,

(x + 9)(x - 4) = 0

Therefore the given equation x² + 5x - 36 has x-intercepts of x = -9 and x = 4 .

What are the x-intercepts of the graph of the function f(x) = x² + 5x - 36?

Summary:

The x-intercepts of the graph of the function f(x) = x² + 5x - 36 are x = -9 and x = 4.