X^2 + 5x + 25/4 is a perfect square trinomial?

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In summary, the conversation discusses converting standard form of a quadratic equation to general form and finding a missing number to make the equation a perfect square trinomial, with the desired answer being 25/4. The student struggles with this problem and receives help from others.
  • #1
EricPowell
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In my pre-calculus math class right now we are learning how to convert the standard form of a quadratic equation to general form. There are just some questions that are about filling in the missing number to make the equation, what I assume to be, a perfect square trinomial. Is that what the question is asking?

The textbook gives the answer as being 25/4. I have no idea how I would go about accomplishing that.

Homework Statement



2) Find a number that makes the expression a perfect square of the form (x+h)^2.

e) x2 + 5x + __



The Attempt at a Solution


I would think that I would have to find a perfect square whose root adds to 5 when multiplied by two. And I can not think of any such number.
 
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  • #2
EricPowell said:
In my pre-calculus math class right now we are learning how to convert the standard form of a quadratic equation to general form. There are just some questions that are about filling in the missing number to make the equation, what I assume to be, a perfect square trinomial. Is that what the question is asking?

The textbook gives the answer as being 25/4. I have no idea how I would go about accomplishing that.

Homework Statement



2) Find a number that makes the expression a perfect square of the form (x+h)^2.

e) x2 + 5x + __

The Attempt at a Solution


I would think that I would have to find a perfect square whose root adds to 5 when multiplied by two. And I can not think of any such number.
Hello EricPowell. Welcome to PF !

Where did you get the 25/4 that's in the title of this thread?
 
  • #3
NEVERMIND
Well now I feel silly...I never thought of thinking of 5/2 as being half of 5. 5/22 is 25/4.
:grumpy:

Thank you for your efforts to help me though!
 
  • #4
EricPowell said:
NEVERMIND
Well now I feel silly...I never thought of thinking of 5/2 as being half of 5. 5/22 is 25/4.
:grumpy:

Thank you for your efforts to help me though!

And you want to write that as (5/2)2, not 5/22, which is equal to 5/4.
 

1. What is a perfect square trinomial?

A perfect square trinomial is an algebraic expression in the form of ax^2 + bx + c, where the coefficient of the squared term (a) is a perfect square and the constant term (c) is also a perfect square.

2. How do you determine if X^2 + 5x + 25/4 is a perfect square trinomial?

To determine if X^2 + 5x + 25/4 is a perfect square trinomial, we can use the formula (a + b)^2 = a^2 + 2ab + b^2. If we can rewrite the given expression as (a + b)^2, then it is a perfect square trinomial. In this case, we can rewrite X^2 + 5x + 25/4 as (x + 5/2)^2, making it a perfect square trinomial.

3. What are the properties of a perfect square trinomial?

The properties of a perfect square trinomial include: having a perfect square as the coefficient of the squared term, having a perfect square as the constant term, and having the same middle term as twice the product of the square root of the coefficient of the squared term and the square root of the constant term.

4. Can a perfect square trinomial have a negative coefficient?

Yes, a perfect square trinomial can have a negative coefficient. As long as the coefficient of the squared term and the constant term are both perfect squares, the trinomial can be considered a perfect square trinomial.

5. How are perfect square trinomials used in mathematics and science?

Perfect square trinomials are used in various mathematical and scientific concepts, such as completing the square, factoring, and solving quadratic equations. They also have applications in geometry, physics, and engineering, where they can be used to model and solve real-world problems.

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