Solve the following polynomial inequality

Question

Solve the following polynomial inequality.

5x²>6x+7

 

please type it in interval notation. type an exact answer using radicals as needed. use integers or fractions for any numbers in the expression. 

 

 

Answer 1

5x² > 6x + 7

 

5x² - 6x - 7 > 0

 

let use quadratic equation:

 

-b ± √b² - 4ac

      2a

 

6 ±√(36 - 4*5*-7)

        10

 

6 ± √176

   10

 

6 ± 4√11

    10

 

3 ± 2√11

    5

 

x > 3 + 2√11                or  x > 3 - 2√11

            5                                      5