Question

consider the trinomial $6x^2 + 13x + 6$. the value of $ac$ is \boxed{4}. the value of $b$ is \boxed{2}. the two numbers that have a product of $ac$ and a sum of $b$ are 4 and \boxed{3}.

Explanation:

Step1: Find \( ac \)

For the trinomial \( ax^2 + bx + c \), here \( a = 6 \), \( c = 6 \). So \( ac = 6\times6 = 36 \).

Step2: Identify \( b \)

In the trinomial \( 6x^2 + 13x + 6 \), the coefficient of \( x \) is \( b \), so \( b = 13 \).

Step3: Find the other number

Let the other number be \( n \). We know that \( 4\times n = 36 \) (since product is \( ac = 36 \)) and \( 4 + n = 13 \) (since sum is \( b = 13 \)). From \( 4 + n = 13 \), we get \( n = 13 - 4 = 9 \). Also, \( 4\times9 = 36 \), which matches the product of \( ac \).

Answer:

First blank: 36; Second blank: 13; Third blank: 9