12 consider the equation 2x21125x find the complex solutions

12.) consider the equation 2x^2-11-25x. find the complex solutions (real and non real) of the equation, and simplify as much as possible. show all work.

Solution

On using the quadratic formula, the roots of the polynomial 2x² -25x -11 are [25 ±{(-25)² -4*2*(-11)]/2*2 or, [25±( 625+88)]/4 or, (25±713)/4. Thus, there are no complex solutions. The real solutions of the given equation are x = (25+713)/4 and x = (25 -713)/4.

Note: As per the quadratic formula, the roots of the polynomial ax² +bx + c are [-b±(b² -4ac)]/2a