solve polynomial inequality and graph the soulution set on a number line 5x^2-3x>8

Question

solve the polynomial inequality and graph the solution set on a number line. express the solution in interval notation.

Answer 1

The polynomial inequality 5x ² -3x > 8

5x ² -3x - 8 > 0

Find the zeros of 5x ² - 3x - 8 = 0

5x ² - 8x  + 5x - 8 = 0

x  (5x  - 8) + 1(5x - 8) = 0

5x - 8 = 0 and x  + 1 = 0

5x  = 8 and x  = -1

x  = 8/5 and x  = -1

x  < -1 and x  > 8/5

Solution in interval notation  (-∞, -1) and (8/5, ∞).