Question

The values of x such that $$2x^2 - 6x + 5 = 0$$

are $m+ni$ and $m-ni,$ where m and n are positive. What is $m\cdot n?$

Answer 1

2x^2-6x+5=0
solving the quadratic above using the quadratic equation we get:
x=[-b+/-sqrt(b^2-4ac)]/2a
plugging the values we get:
x=[6+/-sqrt(36-4*5*2)]/2*2
x=3/2-i/2
or
x=3/2+i/2
thus
m=3/2 and n=1/2
thus
m*n=3/2*1/2=3/4

Answer: 3/4