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

If the roots of x25x+4=0 are p,q, then which of the following CANNOT be the equation with the roots 1/p,1/q ?

A
x45x24=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
4x45x2+1=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4x4+5x2+1=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
x4+5x2+4=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D x4+5x2+4=0
Given that the roots of x25x+4=0 are p,q
Here a=1,b=5,c=4

We know that for
ax2+bx+c=0,a0 with roots p,q
the transformed quadratic equation with roots 1α & 1β is given by:
c(x2)2+b(x)2+a=0

Therefore we can directly write the required equation as:
4(x2)25(x)2+1=0
4x45x2+1=0
Thus, rest all equations are not the correct transformed equation.

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