A training scenario is devised to prepare for a hazardous ma

A training scenario is devised to prepare for a hazardous material (HAZMAT) disaster on Route 95. The police require that all motorists stay at minimum 2 miles away from the disaster zone, located at mile marker 42. Write an absolute value inequality to describe the numbers on the mile markers that police will allow motorists to drive by. Find all complex zeroes of P(x). P(x) = 2x^2 + 6x + 7

Solution

7) P(x) = 2x^2 +6x +7

The discriminat of equation :b^2 -4ac = 6^2 - 4*2*7 = 36 - 56 = -20 ( complex roots)

Using quadratice equation root : x = (-b +/- sqrt(b^2 -4ac)/2a

= ( -6 + /- sqrt( 6^2 -4*2*7)/2*2

= ( -6 +/- sqrt( 36 - 56)/4

= ( -6 +/- sqrt(-20) )/4

= -3/2 +/- isqrt(20)/4

= -3/2 + /- i*sqrt(5)/2

These are the two complex roots of th equation