Question

If (x-2) and(X+3) are factors of x³+ax²+bx-30 find a and b​

Answer 1

Answer:

a=6 and b=-1

Step-by-step explanation:

p(x)=x3+ax2+bx-30

(x-2)=0

x=2

p(2)=0

=(2)^3+a(2)^2+b2-30=0

=8+4a+2b-30=0

=4a+2b=22. (divide by 2)

=2a+b=11 -eq.1

p(-3)=0

=(-3)^3+a(-3)^2+b×(-3)-30=0

=-27+9a-3b-30=0

=9a-3b-57=0

=3a-b-19=0

=3a-b=19 -eq.2

By elimination method

=2a+b=11

=3a-b=19

=5a=30

=a=6

3a-b=19

3×6-b=19

18-b=19

-b=19-18

-b=1

b=-1

To verify:

2a+b=11

2×6-1=11

12-1 =11

11=11. Verified