Question

For the following exercises, find the x -or t -intercepts of the polynomial functions.11. C(t)=4t4+12t3−40t2

Answer: (0,0),(−5,0),(2,0)

Answer 1

Answer: (0,0), (-5,0), (2,0)

Explanation:

c(t)=4t⁴+12t³-40t²

1) t=0

c(t)= 4(0⁴)+12(0³)-40(0²)

c(t)=4(0)+12(0)-40(0²)

c(t)=0+0+0

c(t)=0

Thus (0,0)

2) c(t)=0

4t⁴+12t³-40t²=0

Divide both parts of the equation by 4:

t⁴+3t³-10t²=0

t²(t²+3t-10)=0

t²=0

t=0

Thus (0,0)

t²+3t-10=0

t²+(5t-2t)-10=0

(t²+5t)-(2t+10)=0

t(t+5)-2(t+5)=0

(t+5)(t-2)=0

t+5=0

t=-5

Thus (-5,0)

t-2=0

t=2

Thus (2,0)