Answer :
Answer:
see explanation
Step-by-step explanation:
To find the intercepts equate h to zero, that is
- 16t² + 20t + 6 = 0 ← divide all terms by 2
- 8t² + 10t + 3 = 0 ← multiply through by - 1
8t² - 10t - 3 = 0 ← factor the quadratic
Consider the factors of the product of the coefficient of the t² term and the constant term which sum to give the coefficient of the t- term
product = 8 × - 3 = - 24 , sum = - 10
Factors are - 12 and + 2
Use these factors to split the middle term
8t² - 12t + 2t - 3 = 0 ( factor the first/second and third/fourth terms )
4t(2t - 3) + 1(2t - 3) = 0 ← factor out (2t - 3)
(2t - 3)(4t + 1) = 0
Equate each factor to zero and solve for t
2t - 3 = 0 ⇒ 2t = 3 ⇒ t = [tex]\frac{3}{2}[/tex]
4t + 1 = 0 ⇒ 4t = - 1 ⇒ t = - [tex]\frac{1}{4}[/tex]
Intercepts are (- [tex]\frac{1}{4}[/tex], 0) abd ([tex]\frac{3}{2}[/tex], 0)