At which root does the graph of f(x) = (x + 4)⁶(x + 7)⁵ cross the x axis?

Solution:

If f(x) = (x + 4)⁶ (x + 7)⁵ cross the x-axis,

then y = f(x) = 0.

If f(x) = 0,

then (x + 4)⁶(x + 7)⁵ = 0.

If (x + 4)⁶(x + 7)⁵ = 0,

then x + 4 = 0 and x + 7 = 0

⇒ x = - 4 and x = - 7

Therefore, the roots at which the graph of f(x) = (x + 4)⁶(x + 7)⁵ cross the x axis are -4 and -7.

At which root does the graph of f(x) = (x + 4)⁶(x + 7)⁵ cross the x axis?

Summary:

f(x) = (x + 4)⁶(x + 7)⁵ cross the x axis are -4 and -7. The root at which a curve crosses the y axis can be found by equating x = f(y) = 0. Because on x-axis y coordinate is zero and on y-axis x coordinate is zero.