CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

If x3+ax2+bx+6 divided by x2 as factor then remainder becomes O, and leaves remainder 3 when divided by x3 find the values of a and b.

Open in App
Solution

We are given,
function F(x)=x3+ax2+bx+6
at x=2, we get y=remaindery=0
f(x)=(2)3+a(2)2+b(2)+6=0
4a+2b+14=0(1)
at x=3, we get y=remaindery=3
f(3)=(3)3+4(3)2+b(3)+6=3
27+9a+3b+6=3
9a+3b+30=0(2)
Let, 3×(equation (1))2×(equation (2))
we get,
12a+6b+42=018a+6b+60=0_____________6a18=0
a=3
From eqn (1) b=144a2
b=72a=72(3)=7+6=1
b=1
So, a=3 & b=1

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Remainder Theorem
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon