Answer :

mberisso

Answer:

Answer b. [tex]\frac{225}{4}[/tex]

Step-by-step explanation:

In order to get a perfect square trinomial from a binomial of the form: [tex]x^2 +bx[/tex]. the term to add should be the square of half of the coeficcient "b". That is: [tex](\frac{b}{2} )^2[/tex]. Such will give you a trinomial that comes from the perfect square of the binomial: [tex](x+\frac{b}{2})^2=x^2+bx+(\frac{b}{2}  )^2[/tex]

In your case, b=15 therefore [tex](\frac{b}{2} )^2=(\frac{15}{2} )^2=\frac{225}{4}[/tex]

letmeanswer

Answer:

Option C. The constant is [tex]\frac{225}{4}[/tex]

Solution:

Let us assume that the constant is c.

Now to the equation will be [tex]x^{2}+15 x+c[/tex]-------- (i)

We know the square formula  [tex](a+b)^{2}=a^{2}+2 a b+b^{2}[/tex]

As per the formula we can write the equation as,

[tex]x^{2}+15 x+c[/tex]

[tex]=x^{2}+2 \times x \times\left(\frac{15}{2}\right)+c[/tex]

Now if we need make the equation perfect square,

Then as per the formula c should be [tex]\left(\frac{15}{2}\right)^{2}=\frac{225}{4}[/tex]

And the equation will be the perfect square as [tex]\left(x+\frac{15}{2}\right)^{2}[/tex]

So, the constant is [tex]\frac{225}{4}[/tex]

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