find thecubic eqaution that has a y intercept of (0, -4) and has roots at x=1, x=2, and x= -5
To find the cubic equation that satisfies the given conditions, we can start by assuming an equation of the form:
y = a(x - r)(x - s)(x - t)
Where r, s, and t are the roots of the equation and a is a constant coefficient. In this case, the given roots are r = 1, s = 2, and t = -5. The y-intercept is (0, -4), which means that when x = 0, y = -4.
Using this information, we can substitute the values of x and y into the equation:
-4 = a(0 - 1)(0 - 2)(0 - (-5))
-4 = a(-1)(-2)(5)
-4 = 10a
Solving for a, we find:
a = -4/10
a = -2/5
Now that we have the value of a, we can rewrite the equation as:
y = (-2/5)(x - 1)(x - 2)(x + 5)
Thus, the cubic equation that satisfies the given conditions is:
y = (-2/5)(x - 1)(x - 2)(x + 5)