Between what values is x^2 + 10x - 16 greater than 0.

1 Answer | Add Yours

Top Answer

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The values of x for which x^2 + 10x - 16 is greater than 0 has to be determined.

The inequality x^2 + 10x - 16 > 0 has to be solved.

x^2 + 10x - 16 = 0 gives

x1 = `-10/2 + sqrt (100 + 64)/2`

=> `-5 + sqrt 41`

x2 = `-5 - sqrt 41`

x^2 + 10x - 16 > 0

=> `(x - (-5 + sqrt 41))(x - (-5 - sqrt 41)) > 0`

This is true if both the terms are either greater than 0 or less than 0.

`(x - (-5 + sqrt 41)) > 0 and (x - (-5 - sqrt 41)) > 0`

=> x > `-5 + sqrt 41`

`(x - (-5 + sqrt 41)) < 0 and (x - (-5 - sqrt 41)) < 0`

=> x < `-5 - sqrt 41`

The values of x for which x^2 + 10x - 16 > 0 lie in {-inf., `-5 - sqrt 41` }U{`-5 + sqrt 41` , inf.}

We’ve answered 318,988 questions. We can answer yours, too.

Ask a question