Answer:
r = - 3, r = - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
Given
2r² + 11r + 15 = 0
Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.
product = 2 × 15 = 30 and sum = 11
The factors are + 6 and + 5
Use these factors to split the r- term
2r² + 6r + 5r + 15 = 0 ( factor the first/second and third/fourth terms )
2r(r + 3) + 5(r + 3) = 0 ← factor out (r + 3) from each term
(r + 3)(2r + 5) = 0
Equate each factor to zero and solve for r
r + 3 = 0 ⇒ r = - 3
2r + 5 = 0 ⇒ 2r = - 5 ⇒ r = - [tex]\frac{5}{2}[/tex]
