wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The number of distinct roots of the equation (x5)(x7)(x+6)(x+4)=504 is

A
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is C 4
Given biquadratic equation: (x5)(x7)(x+6)(x+4)=504
Here 5+4=7+6
This equation is of the form (xa)(xb)(xc)(xd)=A, where a+b=c+d

Upon rearranging this equation to the above form we get,
(x5)(x+4)(x7)(x+6)=504;
(x2x20)(x2x42)=504
Assuming x2x20=y, the equation becomes:
y(y22)=504
y222y504=0
Using completing the square method,
y22(11)y+121121504=0
(y11)2=625
y11=±25
y11=25 and y11=25
y=36 and y=14

If y=36
x2x20=36
x2x56=0
x28x+7x56=0
(x8)(x+7)=0x=7,8

If y=14
x2x20=14
x2x6=0
x23x+2x6=0
(x3)(x+2)=0
x=2,3

The roots are 7,2,3,8.
Thus, there are 4 distinct roots of the equation.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Biquadratic Equation of the Form: (x-a)(x-b)(x-c)(x-d)=A, where a+b=c+d
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon