(1) If f(x)= ax
^{3}–9x
^{2}+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 (x^{2}–4x+3) is a factor of cx^{4}+dx^{3}–13x^{2}–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 (x^{2}4x+3).

Posted by Mindrod
on 20060318 13:54:16 