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

If (2x2−3x+1)(2x2+5x+1)=9x2, then equation has

A
four real roots
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
two real and two imaginary roots
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
four imaginary roots
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of the above
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A four real roots
(2x23x+1)(2x2+5x+1)=9x2

(2x23x+1)(2x2+5x+1)x2=9

(2x23x+1)x(2x2+5x+1)x=9

(2x3+1x)(2x+5+1x)=9

(2x+1x3)(2x+1x+5)=9

Let y=2x+1x

(y3)(y+5)=9

y2+2y15=9

y2+2y159=0

y2+2y24=0

(y+6)(y4)=0

(2x+1x+6)(2x+1x4)=0 where y=2x+1x

(2x2+1+6x)(2x2+14x)=0

2x2+6x+1=0,2x24x+1=0

x=6±364×2×12×2,x=4±164×2×12×2

x=6±3684,x=4±1684

x=6±284,x=4±84

x=6±274,x=4±224

x=3±72,x=2±22

Roots are {3+72,372,2+22,222}
Thus, there are four real roots.


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