Use the method described in Relating Concepts Exercises 67–70 if applicable to solve each expiation or inequality.
| x4 + 2x2 + 1| ≥ 0
Exercise 67
For individual or collaborative investigation
To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as |x2 − x | = 6, work Exercise in order.For x2 − x to have an absolute value equal to 6, what are the two possible values that it may be? (Hint: One is positive and the other is negative.)
Exercise 68
For individual or collaborative investigation
To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as |x2 − x | = 6, work Exercise in order.Write an equation stating that x2 − x is equal to the positive value you found in Exercise 67, and solve it using factoring.
Exercise 69
For individual or collaborative investigation
To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as |x2 − x | = 6, work Exercise in order.Write an equation stating that x2 − x is equal to the negative value you found in Exercise 67, and solve it using the quadratic formula. (Hint: The solutions arc not real numbers.)
Exercise 70
For individual or collaborative investigation
To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as |x2 − x | = 6, work Exercise in order.Give the complete sojution set of |x2 − x| = 6, using the results from Exercises 68 and 69.
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