# Find the value of a and b so that (x² -4) is a factor of ax^4+2x³ -3x²+bx-4 . Show the working also

2
by g2000

2014-08-23T14:28:34+05:30
Factor of ax^4+2x³-3x²+bx-4 is (x²-4) or (x-2)(x+2) so the value of the given equation is zero at x = 2 and x = -2, on putting the value of x = 2
16a+16-12+2b-4 = 0
16a+2b = 0
8a+b = 0  ---------------(1)
on putting the value of x = -2
16a-16-12-2b-4 = 0
16a-2b = 32
8a-b = 16  -----------------(2)
(1) + (2)
16a = 16
a = 1
put a = 1 in equation (1) we get
b = -8
I hope you can understand .
2014-08-24T10:00:15+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
X²-4 = (x-2)(x+2)      roots are 2 , -2    So divide by 2, and -2

|  a          2          -3            b            -4
|
2     |            2a        4+4a        2+8a        2b+16a+4
| ____________________________________
|  a      2+2a      1+4a        b+8a+2      2b+16a

So  reminder 2b+16 a = 0     =>    b = -8 a

Similarly, for root -8 :

reminder = -2b-32+16a  = 0    =>  8a - b = 16

solving a = 1 b = -8