wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
Question

Solve the equation
(x+2)(x+3)(x+8)(x+12)=4x2........(1)
find the difference between the rational roots .

Open in App
Solution

Since (2)(12)=(3)(8) we can
write equation (1) as
(x+2)(x+12)(x+3)(x+8)=4x2
(x2+14x+24)(x2+11x+24)=4x2 ...(2)
Now x=0 is not a root of (1)
Dividing by x2 in both sides of (2), we get
(x+24x+14)(x+24x+11)=4 ...(3)
Putting x+24x=y, we get
(y+14)(y+11)=4
y2=25y+150=0
y=15 or y=10
Thus the ariginal equation is equivlent to x+24x=15 or x+24x=10
x2+15x+24=0 or x2+10x+24=0
x=15±1292 or x=6,4
Difference between sational roots is 4(6)=2.

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