Question

if 1 and -2 are zeros of f(x)=xcube+10xsquare+ax+b​

Answer 1

f(x)=x³+10x²+ax+b

let x=1

f(1)=1³+10×1+a+b

f(1)=11+a+b

f(-2)=8+10×(-2)²+a(-2)+b

=48-2a+b

if f(1) =f(-2)=0

11+a+b=0....1

48-2a+b=0.......2

eqn 1-eqn 2

11-48+a+3a=0

4a=37

a=37/4

from eqn 1

b=-11-a=-11-37/4=(-44-37)/4=-81/4

Answer 2

f(x)=x³+10x²+ax+b

let x=1

f(1)=1³+10×1+a+b

f(1)=11+a+b

f(-2)=8+10×(-2)²+a(-2)+b

=48-2a+b

if f(1) =f(-2)=0

11+a+b=0....1

48-2a+b=0.......2

eqn 1-eqn 2

11-48+a+3a=0

4a=37

a=37/4

from eqn 1

b=-11-a=-11-37/4=(-44-37)/4=-81/4.