Question

Quadratic Form Help

Answer 1

\[a ^{8}+10a ^{2}-16
Turn that into quadratic Form. Show me. thanks

Answer 2

@mathstudent55

Answer 3

Are you sure the exponent in the first term is really 8 ?

Answer 4

yes. the directions are to write the expression in quadratic form.

Answer 5

If psble could you take a screenshot and attach. I'm kinda stuck and just want to be doubly sure that the given eqn has no typoes

Answer 6

yes. the directions are to write the expression in quadratic form.

Answer 7

k. one moment!

Answer 8

Ok

Answer 9

Number 12

Answer 10

If you are sure the first term has exponent 8, are you sure the second term has exponent 2?

Answer 11

I see. That is where the "if possible" comes in.

Answer 12

\[a ^{8}+10a ^{2}-16 \]

Answer 13

is it already in quadratic form?

Answer 14

No. It is not. This cannot be written in quadratic form,.

Answer 15

what about number 14? I'm just trying to figure out how to do these problems.

Answer 16

That is why the instructions state "if possible."

Answer 17

For 14., first factor out b.
Then try.

Answer 18

also, what was the reason why the previous one wasnt possible?

Answer 19

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

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

Example:
Write as a quadratic.
4x^6 + 12x^3 + 9
4x^6 = (2x^3)^2, so 4x^6 is the square of something, of 2x^3
9 = 3^2, so 9 is the square of something, of 3
This may be (2x^3 + 3)^2
Now we check the middle term.
The middle term must be the first term times the second term (of the binomial) times 2.
2x^3 * 3 * 2 = 12x^3. Yes the given middle term checks out, so our trinomial is indeed a quadratic.
4x^6 + 12x^3 + 9 = (2x^3 + 3)^2

Answer 20

See my example above.

To see if a trinomial is a binomial squared do this:
1. See if the first term is the square of something. Of what? If it isn't, stop.
2. See if the third term is the square of something. Of what? If it isn't, stop.
3. Multiply the root of the first term by the root of the third term and by 2.
If that gives you the middle term of the original trinomial, then it is a square of a binomial.

Answer 21

Try your example again.

\(a ^{8}+10a ^{2}-16 \)

\(a^8\) is the square of \(a^4\)

\(-16\) is not the square of any real number. Stop.

This is not the square of a binomial.

Answer 22

ok, gtg

Answer 23

After looking this up in a textbook, I realize that I misunderstood the question.
You need to put the polynomial in a form that it shows that it is a quadratic equation. That means you need to rewrite each equation in the form ax^2 + bx + c.

The problem posted:

\(a ^{8}+10a ^{2}-16 \)

can be written as

\((a^4)^2 + 10a^2 -1 6\)

but this is not a quadratic.

We are trying to rewrite the polynomial as a quadratic in a^4.
Since the middle term is a^2, not a^4, it cannot be written as a quadratic.