Question 722541
Quadratic equations are of the form ax^2 + bx + c where a, b and c are integers.  <P>
57 has only four factors:  1 and 57, 19 and 3, and you can see there is no combination that would allow you to easily factor into (2x + d)(x + c).  Another way to check is to look at the discriminant = D = b^2 - 4ac.  If the discriminant is negative then the equation has no real roots, and two non-real, complex roots.<P>
In this equation a=2, b=-20 and c=57.  The discriminant is {{{(-20)^2 - 4*2*57 = 400 - 456 = -56.}}}<P>
Find the solutions/roots using the quadratic formula = {{{(-b + or - D)/2a}}}<P>
{{{(-(-20) + or - sqrt(-50)) / 2a = (20 + or - i*sqrt(50))/4 = 5 + or - (i*sqrt(2*25)/4) = 5 + or - (5/4 * i *sqrt(2))}}}
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