QuestionFind the value of $c$ for which $x^{2}+10x+c$ is a perfect square. Options: A. 100 B. 20 C. 5 D. 25

Studdy Solution

STEP 1

Assumptions1. The polynomial is in the form of a perfect square trinomial. . A perfect square trinomial is in the form (ax+b)^ = a^x^ +abx + b^.
3. We need to find the value of $c$ that makes the polynomial a perfect square trinomial.

STEP 2

In the given polynomial, $x^2 +10x + c$ , we can see that $a^2 =1$ (since coefficient of $x^2$ is1) and $2ab =10$ (since coefficient of $x$ is10).We can use these values to find $b$ .
$b =2ab /2a$

STEP 3

Now, plug in the given values for $a$ and $2ab$ to calculate $b$ .
$b =10 /2$

STEP 4

Calculate the value of $b$ .
$b =10 /2 =$

STEP 5

Now that we have the value of $b$ , we can find the value of $c$ that makes the polynomial a perfect square trinomial. $c$ is equal to $b^2$ .
$c = b^2$

STEP 6

Plug in the value for $b$ to calculate $c$ .
$c =5^2$

STEP 7

Calculate the value of $c$ .
$c =5^2 =25$ The value of $c$ that makes the polynomial a perfect square trinomial is25. So, the correct answer is D.25.

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QuestionFind the value of $c$ for which $x^{2}+10x+c$ is a perfect square. Options: A. 100 B. 20 C. 5 D. 25

Studdy Solution

STEP 1

Assumptions1. The polynomial is in the form of a perfect square trinomial. . A perfect square trinomial is in the form (ax+b)^ = a^x^ +abx + b^.
3. We need to find the value of $c$ that makes the polynomial a perfect square trinomial.

STEP 2

In the given polynomial, $x^2 +10x + c$ , we can see that $a^2 =1$ (since coefficient of $x^2$ is1) and $2ab =10$ (since coefficient of $x$ is10).We can use these values to find $b$ .
$b =2ab /2a$

STEP 3

Now, plug in the given values for $a$ and $2ab$ to calculate $b$ .
$b =10 /2$

STEP 4

Calculate the value of $b$ .
$b =10 /2 =$

STEP 5

Now that we have the value of $b$ , we can find the value of $c$ that makes the polynomial a perfect square trinomial. $c$ is equal to $b^2$ .
$c = b^2$

STEP 6

Plug in the value for $b$ to calculate $c$ .
$c =5^2$

STEP 7

Calculate the value of $c$ .
$c =5^2 =25$ The value of $c$ that makes the polynomial a perfect square trinomial is25. So, the correct answer is D.25.

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QuestionFind the value of ccc for which x2+10x+cx^{2}+10x+cx2+10x+c is a perfect square. Options: A. 100 B. 20 C. 5 D. 25

Studdy Solution

STEP 1

Assumptions1. The polynomial is in the form of a perfect square trinomial. . A perfect square trinomial is in the form (ax+b)^ = a^x^ +abx + b^.3. We need to find the value of ccc that makes the polynomial a perfect square trinomial.

STEP 2

In the given polynomial, x2+10x+cx^2 +10x + cx2+10x+c, we can see that a2=1a^2 =1a2=1 (since coefficient of x2x^2x2 is1) and 2ab=102ab =102ab=10 (since coefficient of xxx is10).We can use these values to find bbb.b=2ab/2ab =2ab /2ab=2ab/2a

STEP 3

Now, plug in the given values for aaa and 2ab2ab2ab to calculate bbb.b=10/2b =10 /2b=10/2

STEP 4

Calculate the value of bbb.b=10/2=b =10 /2 =b=10/2=

STEP 5

Now that we have the value of bbb, we can find the value of ccc that makes the polynomial a perfect square trinomial.ccc is equal to b2b^2b2.c=b2c = b^2c=b2

STEP 6

Plug in the value for bbb to calculate ccc.c=52c =5^2c=52

STEP 7

Calculate the value of ccc.c=52=25c =5^2 =25c=52=25The value of ccc that makes the polynomial a perfect square trinomial is25. So, the correct answer is D.25.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the value of $c$ for which $x^{2}+10x+c$ is a perfect square. Options: A. 100 B. 20 C. 5 D. 25

Assumptions1. The polynomial is in the form of a perfect square trinomial. . A perfect square trinomial is in the form (ax+b)^ = a^x^ +abx + b^.
3. We need to find the value of $c$ that makes the polynomial a perfect square trinomial.

In the given polynomial, $x^2 +10x + c$ , we can see that $a^2 =1$ (since coefficient of $x^2$ is1) and $2ab =10$ (since coefficient of $x$ is10).We can use these values to find $b$ .
$b =2ab /2a$

Now, plug in the given values for $a$ and $2ab$ to calculate $b$ .
$b =10 /2$

Calculate the value of $b$ .
$b =10 /2 =$

Now that we have the value of $b$ , we can find the value of $c$ that makes the polynomial a perfect square trinomial. $c$ is equal to $b^2$ .
$c = b^2$

Plug in the value for $b$ to calculate $c$ .
$c =5^2$

Calculate the value of $c$ .
$c =5^2 =25$ The value of $c$ that makes the polynomial a perfect square trinomial is25. So, the correct answer is D.25.