1
Question
Given that, x2 + 2x - 3 is a factor of x4 + 6x3 + 2ax2 + bx - 3a. Find the values of a and b.
Given that, x2 + 2x - 3 is a factor of x4 + 6x3 + 2ax2 + bx - 3a. Find the values of a and b.
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Solution
x2+2x−3
x2+3x−x−3
x(x+3)−1(x+3)
(x−1)(x+3)
x=1
x=−3
putvalueofxinf(x)
f(x)=x4+6x3+2ax2+bx-3a
when x=1 then
f(×)=1+6+2a+b-3a
f(×)=7-a+b.......eqn1
when ×=-3
f(×)=(-3)^4+6(-3)^3+2a(-3)^2+b(-3)-3a
f(×)=81-162+18a-3b-3a
f(×)=15a-3b-81....eqn2
from eqn1 and eqn2
multiply eqn 1 with 3..we have
3b-3a+21
add this eqn in eqn2
12a-60=0
12a=60
a=5
put value of a in eqn1...we have
7-5+b=0
b=-2
x2+3x−x−3
x(x+3)−1(x+3)
(x−1)(x+3)
x=1
x=−3
putvalueofxinf(x)
f(x)=x4+6x3+2ax2+bx-3a
when x=1 then
f(×)=1+6+2a+b-3a
f(×)=7-a+b.......eqn1
when ×=-3
f(×)=(-3)^4+6(-3)^3+2a(-3)^2+b(-3)-3a
f(×)=81-162+18a-3b-3a
f(×)=15a-3b-81....eqn2
from eqn1 and eqn2
multiply eqn 1 with 3..we have
3b-3a+21
add this eqn in eqn2
12a-60=0
12a=60
a=5
put value of a in eqn1...we have
7-5+b=0
b=-2
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