Quadratic in Form Polynomials Answers
Which equation is equivalent tof(x) = 16x4 – 81 = 0?(4x² - 9)(4x² - 9) = 0✔ (4x² + 9)(4x² - 9) = 0(4x - 9)(4x - 9) = 0(4x + 9)(4x - 9) = 0
Select all of the zeroes of the function.
Solve x4 – 17x2 + 16 = 0.Let u = x17x²✔ x²-17x².
Rewrite the equation in terms of u. u² - 17u - 16 = 017u² + u + 16 = 0-u² + 17u + 16 = 0✔ u² - 17u + 16 = 0
Factor. (u + 16)(u + 1) = 0✔ (u - 16)(u - 1) = 0(u + 17)(u - 1) = 0
Select all of the solutions to the original equation.
Solve (x + 3)2 + (x + 3) – 2 = 0.Let u = x✔ x + 3(x + 3)²x²
Rewrite the equation in terms of u.
Factor the equation. ✔ (u + 2)(u – 1) = 0(u + 1)(u – 2) = 0(u – 2)(u – 1) = 0
What are the solutions of the original equation?x = 1 or x = –2x = –1 or x = 2✔ x = –5 or x = –2x = 4 or x = –5
What are the solutions of 4x4 – 4x2 = 8?
Solve the equation 6(2x + 4)2 = (2x + 4) + 2.
Solve (x + 4)2 – 3(x + 4) – 3 = 0 using substitution.u = x✔ x + 43(x + 4)(x + 4)²
Select the solution(s) of the original equation.
Is the equation x9 – 5x3 + 6 = 0 quadratic in form? Explain why or why not.
No. It is not quadratic in form because (x³)² = x⁶, not x⁹, so the variable part of the first term is not the square of the variable part of the second term.
Examine the criteria below. Check which of these you included in your response.
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