Question

X^2 +2x-3 is a factor of x^4+6x^3+2ax^2+bx-3a then find the values of a and b

Answer 1

​x​2​​+2x−3​
x​2​​+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
verify ans by putting value of a and b in f(×)

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