Quadratic in Form Polynomials

Question 1

What substitution should be used to rewrite 4x4 – 21x2 + 20 = 0 as a quadratic equation?

Revolt · Accepted Answer

u = x2

Question 2

What substitution should be used to rewrite 4x12 – 5x6 – 14 = 0 as a quadratic equation?

Revolt · Accepted Answer

u = x6

Question 3

Which quadratic equation is equivalent to (x – 4)2 – (x – 4) – 6 = 0?

Revolt · Accepted Answer

u2 – u – 6 = 0 where u = (x – 4)

Question 4

Which quadratic equation is equivalent to (x2 – 1)2 – 11(x2 – 1) + 24 = 0?

Revolt · Accepted Answer

u2 – 11u + 24 = 0 where u = (x2 – 1)

Question 5

Which quadratic equation is equivalent to (x + 2)2 + 5(x + 2) – 6 = 0?

Revolt · Accepted Answer

u2 + 5u – 6 = 0 where u = (x + 2)

Question 6

What substitution should be used to rewrite 16(x3 + 1)2 – 22(x3 + 1) – 3 = 0 as a quadratic equation?

Revolt · Accepted Answer

u = (x3 + 1)

Question 7

What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.

Revolt · Accepted Answer

and x = ±10i

Question 8

What are the solutions of the equation x4 – 9x2 + 8 = 0? Use u substitution to solve.

Revolt · Accepted Answer

x = ±1 and

Question 9

What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.

Revolt · Accepted Answer

and x = ±i

Question 10

What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) – 4 = 0 as a quadratic equation?

Revolt · Accepted Answer

u = (x + 5)

Quadratic in Form Polynomials Answers