Question

Which of the following constants can be added to x^2+15x to form a perfect square trinomial?

Answer 1

Answer:

Answer b. $\frac{225}{4}$

Step-by-step explanation:

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

In your case, b=15 therefore $(\frac{b}{2} )^2=(\frac{15}{2} )^2=\frac{225}{4}$

Answer 2

Answer:

Option C. The constant is $\frac{225}{4}$

Solution:

Let us assume that the constant is c.

Now to the equation will be $x^{2}+15 x+c$-------- (i)

We know the square formula  $(a+b)^{2}=a^{2}+2 a b+b^{2}$

As per the formula we can write the equation as,

$x^{2}+15 x+c$

$=x^{2}+2 \times x \times\left(\frac{15}{2}\right)+c$

Now if we need make the equation perfect square,

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

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

So, the constant is $\frac{225}{4}$