find the values of p and q so that 1 and -2 are the zeroes of the polynomial x^3+10x^2+px+q
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p(1)=1^3+10×1^2+p+q
p+q+11=0
p+q=-11......... eq (1)
again
p(-2)=(-2)^3+10×(-2)^2+2×p+q
0=-8+40+2p+q
2p+q=-32...... eq (2)
eq (1)-(2)
;p-2p=-11+32
;p=-21
put p=-21 in eq (1)
-21+q=-11
;q=-11+21
;q=10
q=10 and p=-21
is your answer
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p+q+11=0
p+q=-11......... eq (1)
again
p(-2)=(-2)^3+10×(-2)^2+2×p+q
0=-8+40+2p+q
2p+q=-32...... eq (2)
eq (1)-(2)
;p-2p=-11+32
;p=-21
put p=-21 in eq (1)
-21+q=-11
;q=-11+21
;q=10
q=10 and p=-21
is your answer
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