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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0



Answer :

sqdancefan

Answer:

  • x^4 – 6x^2 – 27 = 0
  • 6(2x + 4)^2 = (2x + 4) + 2
  • 6x^4 = -x^2 + 5

Step-by-step explanation:

You want to identify the equations that are quadratic in form.

Quadratic

A polynomial equation is "quadratic in form" if the powers of the variables are integer multiples of {0, 1, 2}, or some subset of these that includes 2. That is, it will be "quadratic" if some substitution z = f(x) is possible such that the resulting equation in z is a polynomial equation of degree 2.

x^4 – 6x^2 – 27 = 0

Term are degrees 0, 2, 4, so this is "quadratic in form". The substitution z=x^2 will give a quadratic in z.

3x^4 = 2x

Term degrees are 1 and 4, so this is not quadratic.

2(x + 5)^4 + 2x^2 + 5 = 0

The substitution z = (x+5)^2 is suggested by the 4th-power term, but the remaining terms cannot be written as a linear function of z. This is not quadratic.

6(2x + 4)^2 = (2x + 4) + 2

This is a straight quadratic equation. One could substitute z=2x+4, but that is not necessary. This is "quadratic in form."

6x^4 = -x^2 + 5

Term degrees are 0, 2, 4, so this is "quadratic in form."

8x^4 + 2x^2 – 4x = 0

Term degrees are 1, 2, 4, so this is not quadratic.

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