Question

WHAT VALUE OF C MAKES THE POLYNOMIAL A PERFECT SQUARE TRINOMIAL 4X^2-28X+C

Answer 1

I don't understand the question. Can you check on the exact wording of the problem?

Answer 2

Is the word "root" supposed to be there?

Answer 3

I CHANGED IT

Answer 4

Good.
A perfect square trinomial is like the following two patterns:

\((a + b)^2 = a^2 + 2ab + b^2 \)

\((a - b)^2 = a^2 - 2ab + b^2 \)

Answer 5

Since your middle term is -28x, we are following the second pattern.

Answer 6

OKAY

Answer 7

Notice that in the second pattern,
the trianomial
\(a^2 - 2ab + b^2 = (a - b)^2 \)

In the trinomial you have \(a^2)\, but the squared binomial has only a, as in a + b.

Answer 8

DONT WANT TO PRESSURE YOU BUT CAN YOU HURRY ITS BECAUSE I ONLY GET CURTAIN AMOUNT OF TIME FOR EACH PROBLEM

Answer 9

We can start writing what the binomial has to be:

\(4x^2 - 28x + c = (2x - ~?~)^2 \)

Answer 10

We need to figure out what goes in the ?

Answer 11

It has to be a number that when you square you get c.

Answer 12

16

Answer 13

OR 13

Answer 14

Also, the middle term of the trinomial is -2ab,
so -2ab = -28x, and a = 2x
-2ab = -2(2x)b = -28x
-4xb = -28x
xb = 7x
b = 7
Since b = 7, c = 49

\(4x^2 - 28x + 49 = (2x - 7)^2\)

c = 49

Answer 15

WOULD IT BE (2X-7)^2 OR (2X+7)(2X-7)

Answer 16

We are not dealing with a difference of squares which is the product of a sum and a difference.

This is the square of a binomial, so it is \( (2x - 7)^2 \)