Question
Sun September 15, 2013 By: Srishti Mallick
 

For which values of a and b, are the zeroes of q(x) = x(cube)+2x(sq)+a also the zeroes of the polynomial p(x) = x(power 5)-x(power 4)-4x(cube)+ 3x(sq)+3x+b? Which zeroes of p(x) are not the zeroes of q(x)?

Expert Reply
Mon September 16, 2013
 
Thus, we have:
p(x) = (x² - 3x + 2).q(x)
and thus would the roots of q(x) will also be roots of p(x).

And the roots of p(x) that are not roots of q(x) are evidently the roots of:
x² - 3x + 2 = 0
x² - 2x - x + 2 = 0
x(x - 2) - (x - 2) = 0
(x - 2)(x - 1) = 0
And they are x=1 or x=2
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