Consider the trinomial [tex]\( 6x^2 + 13x + 6 \)[/tex].
1. Determine the value of [tex]\( ac \)[/tex]:
- Here, [tex]\( a = 6 \)[/tex] and [tex]\( c = 6 \)[/tex].
- So, the value of [tex]\( ac \)[/tex] is [tex]\( a \times c = 6 \times 6 = 36 \)[/tex].
2. Determine the value of [tex]\( b \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] in the trinomial is [tex]\( 13 \)[/tex].
- Thus, the value of [tex]\( b \)[/tex] is [tex]\( 13 \)[/tex].
3. Find two numbers that have a product of [tex]\( ac \)[/tex] and a sum of [tex]\( b \)[/tex]:
- We need two numbers whose product is [tex]\( 36 \)[/tex] (since [tex]\( ac = 36 \)[/tex]) and whose sum is [tex]\( 13 \)[/tex] (since [tex]\( b = 13 \)[/tex]).
- The two numbers that satisfy these conditions are [tex]\( 4 \)[/tex] and [tex]\( 9 \)[/tex], since [tex]\( 4 \times 9 = 36 \)[/tex] and [tex]\( 4 + 9 = 13 \)[/tex].
Therefore, the values are:
- The value of [tex]\( ac \)[/tex] is [tex]\( 36 \)[/tex].
- The value of [tex]\( b \)[/tex] is [tex]\( 13 \)[/tex].
- The two numbers that have a product of [tex]\( ac \)[/tex] and a sum of [tex]\( b \)[/tex] are [tex]\( 4 \)[/tex] and [tex]\( 9 \)[/tex].
To summarize:
[tex]\[
\text{The value of } ac \text{ is } 36.
\][/tex]
[tex]\[
\text{The value of } b \text{ is } 13.
\][/tex]
[tex]\[
\text{The two numbers that have a product of } ac \text{ and a sum of } b \text{ are } 4 \text{ and } 9.
\][/tex]
