Answer :
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]
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]