P and N intercepts of a function

Question

Given the function  P(t)=3t^4−24t^3+21t^2

P intercept is:

T intercepts are:

Answer 1

P intercept is the value of P(t) when t = 0:

 

3(0)^4 - 24(0)^3 + 21(0)^2 = 0 

 

T intercepts is when P(t) = 0:

 

0 =  3t^4 -24t^3 +21t^2      or     0  =  t^2 -8 t + 7      We divided both sides by 3t^2

 

The T intercepts are the zeros of this quadratic equation:   t^2 - 8 t + 7 = 0      

 

                                                                                     (t - 7)(t - 1) = 0

 

 The T intercepts are:  t = 7  and t = 1                                                 

Answer 2

P intercept is the same as y-intercept.  Simply evaluate P(t) when t=0.  This part you should be able to do.

 

T intercepts are the same as x-intercepts.  Simplify evaluate t when P(t)=0.  You many need to use the quadratic formula to find t.

 

First, we need to factor P(t) to easily find the T intercepts.

 

P(t) = 3t²(t² - 8t + 7)

 

0 = 3t²(t² - 8t + 7)

 

 

Then set the factors equal to zero.

 

3t² = 0                    and                  t² - 8t + 7 = 0

 

 

Now solve for t from both equations.