Factor 3x2-4x+14

Question

How do I factor this?

Answer 1

Factor 3x2-4x+14

 

For this you have to use the quadratic formula.

For the quadratic expression, ax^2 + bx + c = 0. the solutions for x are given by,

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

for our quadratic expression 3x^2 - 4x + 14, a = 3, b = -4, c = 14, giving,

x = (4 +/- sqrt(16 - 12*14)) / 6 = (4 +/- sqrt(16 - 168) / 6 = (4 +/- sqrt(-152)) / 6 = (4 +/- 2.i.sqrt(38)) / 6 = 2/3 +/- (i/3)*sqrt(38)

Therefore, x = 2/3 - (i/3)*sqrt(38), x = 2/3 + (i/3)*sqrt(38)     (where i - sqrt(-1))

Our original expression then factorises as: (3x - 2 + i.sqrt(38))(3x - 2 - i.sqrt(38)) / 3