Question

What value for c will make the expression a perfect square trinomial? x2 – 7x + c

Answer 1

Answer:

Final answer is $\frac{49}{4}$.

Step-by-step explanation:

Given expression is $x^2-7x+c$.

Now we need to find about what value for c will make the given expression $x^2-7x+c$, a perfect square trinominal.

Coefficient of middle term that contains x, in $x^2-7x+c$ -7.

Take half of that so we get $-\frac{7}{2}$.

Then take square of the half value.

We get $\left(-\frac{7}{2}\right)^2=\frac{49}{4}$.

We add the square value to make perfect square trinomial.

Hence final answer is $\frac{49}{4}$.

Answer 2

Answer:

D. $\frac{49}{4}$.

Step-by-step explanation:

We have been given a trinomial $x^2-7x+c$. We are asked to find the value of c, which will make the expression a perfect square trinomial.

We know that a perfect trinomial is in form $a^2\pm2ab+b^2$.

We will use complete the square process to solve for c.

To complete a square, we need to add square of half the coefficient of x term. We can see that coefficient of x is -7, so the value of c would be:

$(\frac{b}{2})^2=(\frac{-7}{2})^2=\frac{(-7)^2}{2^2}=\frac{49}{4}$.

Therefore, the value of c required to make the given expression a perfect trinomial is $\frac{49}{4}$ and option D is the correct choice.