Quadratic In Form Polynomials

8 September 2022
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10 test answers

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question
Which quadratic equation is equivalent to (x-4)^2 - (x-4) - 6 = 0?
answer
u^2 - u - 6= 0 where u= (x - 4)
question
What substitution should be used to rewrite 4x^12 - 5x^6 - 14 = 0 as a quadratic equation?
answer
u = x^6
question
What substitution should be used to rewrite 6(x + 5)^2 + 5(x + 5) - 4 = 0 as a quadratic equation?
answer
u = (x + 5)
question
What substitution should be used to rewrite 4x^4 - 21x^2 + 20 = 0 as a quadratic equation?
answer
u = x^2
question
Which quadratic equation is equivalent to (x^2 - 1)^2 - 11(x^2 - 1) + 24 = 0?
answer
u^2 - 11u + 24 = 0 where u = (x^2 - 1)
question
What are the solutions of the equation x^4 + 6x^2 + 5 = 0? Use u substitution to solve.
answer
x = +/- square root of -1 and x = +/- square root of -5
question
Which equation is in quadratic form?
answer
10x^8 + 7x^4 + 1 = 0
question
What are the solutions of the quadratic equation (x - 8)^2 - 13(x - 8) + 30 = 0? Use u substitution to solve.
answer
x = 11 and x = 18
question
Which quadratic equation is equivalent to (x + 2)^2 + 5(x + 2) - 6 = 0?
answer
u^2 + 5u - 6 = 0 where u = (x + 2)
question
What are the solutions of the equation x^4 - 5x^2 - 14 = 0? Use factoring to solve.
answer
x = +/- square root of 7 and x = +/- i square root 2