June 2010 ACT Math- Question

<p>Question#60
Susan Discovered by trail and error that one root of the equation 2x^3 - 9x^2 + 16x - 12 =0
is 2 what are the other roots?</p>

<p>A. (5/4) +/- sqrt23/4
B. (5/2) +/- sqrt23/4
C. (5/4) +/- i sqrt23/2
D. (5/4) +/- i sqrt23/4
E. -(5/4) +/- i sqrt23/4</p>

<p>The answer is D.</p>

<p>How do you do this problem???</p>

<p>Use synthetic division to divide by (x-2) , one of the known roots.</p>

<p>(x-2) l 2 l -9 l 16 l -12
0 4 -10 12
2 -5 6 0</p>

<p>Therefore your factored equation is (x-2)(2x^2 - 5x + 6) = 0
9
Now take the second factored equation and apply the quadratic formula</p>

<p>(5 +/- sqrt(25-4(2)(6)) ) / 2(2) =</p>

<p>(5 +/- sqrt(-23))/4 =</p>

<p>(5 +/- i sqrt(23))/4 =</p>

<p>5/4 +/- i sqrt(23)/4</p>

<p>D</p>

<p>im assuming you understand synthetic divison. Knowing how to use it is a huge help in factoring polynomials.</p>

<p>aww shazeline you stole my thunder! i was so excited to explain synthetic division lol</p>