Question

Find the coordinates of all points where the curve y=x³+2x-15x cuts the x-axis

Answer 1

To find the coordinates of the points where the curve intersects the x-axis, we need to set y equal to zero (since the y-coordinate of any point on the x-axis is always zero) and solve for x.

Setting y = 0 in the equation y = x³ + 2x - 15x, we have:

0 = x³ + 2x - 15x

Simplifying this expression, we get:

0 = x³ - 13x

Factor out an x:

0 = x(x² - 13)

Setting each factor equal to zero:

x = 0
x² - 13 = 0

For x = 0, the y-coordinate is also 0, so the first point where the curve intersects the x-axis is (0, 0).

For x² - 13 = 0, we can solve this equation for x by taking the square root of both sides:

x² = 13
x = ±√13

So, the curve intersects the x-axis at the points (√13, 0) and (-√13, 0).