How to find answer with synthetic division
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You problably mean 2x3+3x2-12x-45=0 because the given equation has no rational roots and synthetic division would be unsuitable. If there is a rational root (making synthetic division feasible) then it's probably a factor of 45, which has 3 and 5 as its factors.

When x=3, we have 54+27-36-45=0, therefore x-3 is a factor and we can divide by this zero using synthetic division:

3 | 2 3 -12 | -45

     2 6  27 |  45

     2 9  15 |   0 = 2x2+9x+15 which has complex roots:

2x2+9x+15=0,

x2+4.5x=-7.5,

x2+4.5x+5.0625=-7.5+5.0625=-2.4375,

(x+2.25)2=-2.4375=-39/16.

x+2.25=±i√39/4=±1.56125i approx, x=-2.25+1.56125i, or -2.25-1.56125i.

So the roots are 3 and -2.25+1.56125i, and -2.25-1.56125i.

by Top Rated User (1.2m points)

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