Question

find the values of p and q so that 1and -2 are zeroes of the polynomial x3+10x2+px+q

Answer 1

hope this answer helps

Answer 2

x³+10x²+px+q

1 and -2 are zeroes of the given polynomial.

Put x = 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

(-2)³+10(-2)²+p(-2)+q = 0

-8+10(4)-2p+q = 0

-8+40-2p+q = 0

32-2p+q = 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

q = -18

Therefore, p = 7 and q = -18

Hope it helps