Perform the operation. Express the answer in reduced form. f(x)=2x2+x+62 Write your answer in the form of the ratio of polynomials p(x)q(x), where p(x)q(x) is

Question

simplifiest form

Answer 1

2x^2 +x +62 = p(x)q(x) = product of imaginary irrational factors

= (x+.25-.75isqr55)(x+.25+.75isqr55)

=(2x+.5 -1.5isqr55 )(x+.75isqr55 )

x =-1/4 + or - .25sqr(1-496) = -.25 +/-.25isqr495

= .25 +/-.75isqr55

it's an upward opening parabola, vertex = minimum point = (-1/4, 61 7/8), with no x intercept = no real roots, y intercept 62. use the quadratic formula to find the imaginary roots, then change their signs, stick an x in front and multiply the factors