given the function ( g(t) = 3t^{4}-24t^{3}+45t^{2} ) its ( g )-intercept is enter a point more.. its ( t…

Explanation:

Step1: Find the (g)-intercept

The (g)-intercept occurs when (t = 0). Substitute (t=0) into (g(t)): (g(0)=3\times0^{4}-24\times0^{3}+45\times0^{2}=0) So the (g)-intercept is the point ((0,0))

Step2: Find the (t)-intercepts

The (t)-intercepts occur when (g(t) = 0). Set (g(t)=3t^{4}-24t^{3}+45t^{2}=0) Factor out (3t^{2}): (3t^{2}(t^{2}-8t + 15)=0) Factor the quadratic (t^{2}-8t + 15=(t - 3)(t - 5)) So (3t^{2}(t - 3)(t - 5)=0) Using the zero - product property: (3t^{2}=0) gives (t = 0); (t-3=0) gives (t=3); (t - 5=0) gives (t=5) The (t)-intercepts are the points ((0,0)), ((3,0)), ((5,0))

Answer:

The (g)-intercept is ((0,0)). The (t)-intercepts are ((0,0)), ((3,0)), ((5,0))