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

Consider the cubic equation x3+px2+qx+r=0, where p, q, r are real numbers.
Which of the following statements is correct?

A
If p22q<0, then the equation has one real and two imaginary root.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
If p22q0, then the equation has all real roots.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
If p22q>0, then the equation has all real and distinct roots.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
If 4p327q2>0, then the equation has real and distinct roots.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A If p22q<0, then the equation has one real and two imaginary root.
Let f(x)=x3+px2+qx+r
f(x)=3x2+2px+q
Disc =4p212q=4(p23q)
=4(p22qq)
If p2<2qp2<3q
So, the equation f(x)=0 has one real and two imaginary roots.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Conjugate of a Complex Number
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon