Thread: Quadratic Form - Making my hair fall out

I did not come here for quick answers. I've just been trying this for a long time to no avail. Help would be much appreciated.

Write the expression 3x^24 + 4x^ 12 + 7 in quadratic form.

A: 3x^24 + 4x^12 + 7 ?

Write the expression -5x^4 - 10x + 6 in quadratic form.

A: -5(x^2 * x^2) - 10x^2 + 6 ?

Originally Posted by dxdy

I did not come here for quick answers. I've just been trying this for a long time to no avail. Help would be much appreciated.

Write the expression 3x^24 + 4x^ 12 + 7 in quadratic form.

A: 3x^24 + 4x^12 + 7 ?

let u = x^12 ...

3u^2 + 4u + 7

Write the expression -5x^4 - 10x + 6 in quadratic form.

is it supposed to be -5x^4 - 10x^2 + 6 ??

.

Originally Posted by skeeter

is it supposed to be -5x^4 - 10x^2 + 6 ??

Doh. Yes it is supposed to be -5x^4 - 10x^2 + 6. My fault.

Options for 3x^24 + 4x^12 + 7 are:
(A) 3(x^12 * x^2) + 4x^12 + 7
(B) 3x^24 + 4(x^24 * x^1/2) + 7
(C) -5 (x^2)^2 - 10x^2 + 6
(D) -5(x^2 * x^2) - 10x + 6

Options for -5x^4 - 10x^2 + 6 are:
(A) -5x^4 + 10(x^4)^1/2 + 6
(B) -5x^4 + 10(x^4 * x^1/2) + 7
(C) 3(x^12)^2 + 4^12 + 7
(D) 3x^24 + 4(x^24)^1/2 + 7

Originally Posted by dxdy

Write the expression 3x^24 + 4x^ 12 + 7 in quadratic form.

Write the expression -5x^4 - 10x^2 + 6 in quadratic form.

To learn how to recognize (and then factor) these sort-of quadratics, try here.

Short version: If you have two variable terms and the power on the one term's variable is twice the power on the other term's variable, you have something of quadratic "form". That is, if you have ax^(2m) + bx^(m) + c, then you have a quadratic in x^m: a(x^m)^2 + b(x^m) + c.