Question

find p and q so that 1 and -2 are zeros of the polynomial p(x)=x3+10x2+px+q

Answer 1

since 1 is the zero...its satisfies the polynomial...


p(1)=1+10+p+q=0

p+q=-11-------(1)

and p(-2)=0

-8+40-2p+q=0

32=2p-q ---------(2)

solving (1) and (2)

p=7,q=-18



I hope this will help u ;)

Answer 2

p(x)=x³+10x²+px+q
1 and -2 are two zeroes
Put x=1,
p(1)=(1)³+10(1)²+p(1)+q=0
1+10+p+q=0
p+q+11=0
p+q= -11 ———(1)

put x= -2,
p(-2)=(-2)³+10(-2)²+p(-2)+q=0
-8+10(4)-2p+q=0
-8+40-2p+q=0
-2p+q+32=0
-2p+q=-32————(2)

(1)-(2)
p+q=-11
-2p+q= -32
________
3p=21
p=21/3
p=7

p+q=-11
7+q= -11
q=-11-7=-18
p=7,q= -18