Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To determine the value of \( c \) that makes the expression \( x^2 - 12x + c \) a perfect square trinomial, we need to consider what it means for a quadratic expression to be a perfect square trinomial. A perfect square trinomial is of the form \( (x + a)^2 \), which expands to \( x^2 + 2ax + a^2 \).
Given the expression \( x^2 - 12x + c \), we can compare it to the general form \( x^2 + 2ax + a^2 \). Notice that the term \( -12x \) corresponds to \( 2ax \) in the perfect square form.
To find the value of \( a \):
[tex]\[ 2a = -12 \][/tex]
Dividing both sides by 2:
[tex]\[ a = -6 \][/tex]
Now, we find \( c \) by squaring \( a \):
[tex]\[ c = a^2 \][/tex]
[tex]\[ c = (-6)^2 \][/tex]
[tex]\[ c = 36 \][/tex]
Therefore, the value of \( c \) that makes the expression \( x^2 - 12x + c \) a perfect square trinomial is \( 36 \).
So, the correct value of \( c \) is:
[tex]\[ 36 \][/tex]
Given the expression \( x^2 - 12x + c \), we can compare it to the general form \( x^2 + 2ax + a^2 \). Notice that the term \( -12x \) corresponds to \( 2ax \) in the perfect square form.
To find the value of \( a \):
[tex]\[ 2a = -12 \][/tex]
Dividing both sides by 2:
[tex]\[ a = -6 \][/tex]
Now, we find \( c \) by squaring \( a \):
[tex]\[ c = a^2 \][/tex]
[tex]\[ c = (-6)^2 \][/tex]
[tex]\[ c = 36 \][/tex]
Therefore, the value of \( c \) that makes the expression \( x^2 - 12x + c \) a perfect square trinomial is \( 36 \).
So, the correct value of \( c \) is:
[tex]\[ 36 \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.