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3. for which values of a and b are the zeroes of q (x) =x 3 +2x 2 +a also the zeroes of tyhe polynomial p(x) = x 5 – x 4 – 4x 3 + 3x 2 +3x +b ? which zeroes of p(x) are not the zeroes of q(x) ?
Indirectly they are telling u that p(x) is divisible by q(x).If u divide p(x) by q(x) u will get a remainder (-(a+1)x^2)+3(a+1)x+b-2a=0.As the remainder is 0, -(a+1)=0,b-2a=0By solving we get a=(-1) b=2In the division we get a quotient (x^2)-3x+2 Zero of this polynomial is 2,1Thus 2,1 are zeroes of p(x) but not of q(x)
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