Hi

y^2 + bx + c with roots -1 ± 4i

Referring to the Quadratic formula



b = 1



thus

b^2 - 4ac = -16

 1 -4*1*c = -16

   17 = 4c

   17/4 = c 

Answer by CharlesG2(834)   (Show Source): You can put this solution on YOUR website!
 A parabola of the form y=2x squared+bx+c has complex roots of -1plus/minus 4i.  Find the values of b and c





y = 2x^2 + bx + c

roots -1 +- 4i

x1 = -1 + 4i

x2 = -1 - 4i

x1 and x2 are conjugates (opposite signs on imaginary parts)

-1 + 4i - x1 = 0 --> -x1 = 1 - 4i

-1 - 4i - x2 = 0 --> -x2 = 1 + 4i

(x + 1 - 4i)(x + 1 + 4i)

x^2 + x + 4ix + x + 1 + 4i - 4ix - 4i - 16i^2, i^2 = -1

4ix cancels out, 4i cancels out

x^2 + 2x + 1 + 16

x^2 + 2x + 17 --> that does not match up to form 2x^2 + bx + c so:

y = 2x^2 + 4x + 34 (multiplied each term by 2)

b = 4, c = 34

check:

(-1 + 4i)^2 = (-1 + 4i)(-1 + 4i) with FOIL = 1 - 8i + 16i^2 = 1 - 8i - 16

(-1 + 4i)^2 = -15 - 8i

(-1 - 4i)^2 = (-1 - 4i)(-1 - 4i) with FOIL = 1 + 8i + 16i^2 = 1 + 8i - 16

(-1 + 4i)^2 = -15 + 8i

4(-1 + 4i) = -4 + 16i

4(-1 - 4i) = -4 - 16i

y = 2(-15 - 8i) - 4 + 16i + 34 = -30 - 16i - 4 + 16i + 34 = -34 + 34 = 0, yes

y = 2(-15 + 8i) - 4 - 16i + 34 = -30 + 16i - 4 - 16i + 34 = -34 + 34 = 0, yes

 

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