Question

find the value of a and b so that the polynomial x3 - ax2 - 13x +b has x-1 and x+3 as factors

Answer 1

x-1=0    ,       x+3=0
x=1       ,       x= -3
p(x)=x3-ax2-13x+b
p(1)=(1)3-a(1)2-13×1+b
=1-a-13+b
=a-12+b
=a=12-b

p(-3)=(-3)3-a(-3)2-13(-3)+b
=-27-9a+39+b
=12-9a+b
=b=9a-12
b=9(12-b)-12
b=108-9b-12
b=96-9b
b+9b=96
10b=96
b=96/10
b=9.6
a=12-b
a=12-9.6
a=2.4
i hope it helps you

Answer 2

Answer:

a=2.4 ; b=96/10

Step-by-step explanation:

x-1=0    ,       x+3=0

x=1       ,       x= -3

p(x)=x3-ax2-13x+b

p(1)=(1)3-a(1)2-13×1+b

=1-a-13+b

=a-12+b

=a=12-b

p(-3)=(-3)3-a(-3)2-13(-3)+b

=-27-9a+39+b

=12-9a+b

=b=9a-12

b=9(12-b)-12

b=108-9b-12

b=96-9b

b+9b=96

10b=96

b=96/10

b=9.6

a=12-b

a=12-9.6

a=2.4