(1) If f(x)= ax³–9x²+bx+12 has x+1 and 2x–3 as factors, then find the values of a and b (without using the actual process of Division of Polynomials).

(2) If (x²–4x+3) is a factor of cx⁴+dx³–13x²–14x+24, then find the values of c and d (without using the actual process of Division of Polynomials).

(In reply to Possible "how to" by e.g.)

I'm sure your method will work.  Let's try (1):

3*f(-1 )  =    -3a - 27    - 3b + 36 = 0;
2*f(1.5) = 6.75a - 40.5 + 3b + 24 = 0;

adding:     3.75a -67.5         + 60  = 0

solve for a:     a = (67.5 - 60)/3.75 = 2

by substitution:  -3(2) - 27 - 3b + 36 =0 yields b = 1  

Easily done.  Part (2) can be done the same way, after using the quadratic formula to find the two roots of (x²-4x+3).

Posted by Mindrod on 2006-03-18 13:54:16