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Solve the quadratic inequality algebraically.

2x²-4x-5 > 0

User Ben Usman
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1 Answer

20 votes
20 votes

Answer:

x < 1 -(√14)/2 or

1 +(√14)/2 < x

Explanation:

You want an algebraic solution to the inequality 2x²-4x-5 > 0.

Completing the square

We can factor out the leading coefficient from the variable terms and subtract the constant term to get ...

2(x² -2x) > 5

Dividing by 2 and adding 1 to complete the square, we have ...

x² -2x +1 > 5/2 +1

(x -1)² > 7/2

Solutions

Taking the square root gives us the pair of inequalities ...

-(√14)/2 > x -1 or

x -1 > (√14)/2

Adding 1 completes the solution

x < 1 -(√14)/2 or

1 +(√14)/2 < x

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Additional comment

A quadratic inequality of the form z² > c is not so different from an absolute value inequality of the form |z| > c. Each resolves to two inequalities with disjoint solution sets.

Solve the quadratic inequality algebraically. 2x²-4x-5 > 0-example-1
User Zarkone
by
2.8k points