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ohaa [14]
3 years ago
11

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

Mathematics
2 answers:
ANEK [815]3 years ago
7 0

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}.

nordsb [41]3 years ago
3 0

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.

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