Question

if (x-2) and (x+3) are factors of x³ + ax² +bx -30, finds a and b

Answer 1

Answer:

a=6 , b= -1.

Step-by-step explanation:

f(x) = x^3+ax^2+bx-30

x-2=0

x=2

in f(x),

8+4a+2b-30=0

4a+2b=-22 ---------(1)

x+3=0

x=-3

in f(x),

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

9a-3b=57 -----------(2)

by solving the linear equations we get

a=6

b= -1

Answer 2

Answer:

Step-by-step explanation:

substitute x=2,x=-3

(2)^3+a(2)^2+b(2)=30

=8+4a+2b=30

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

=-22+4a+2b=0

=4a+2b=22.

now substitute x=-3

(-3)^3+a(-3)^2+b(-3)=30

-27+9a-3b=30

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

=-57+9a-3b=0

=9a-3b=57.

ELIMINTION_

4a+2b=22

9a-3b=57

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