1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# In the quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then, the equation p[p(x)]=0 has

A

Only purely imaginary roots

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B

All real roots

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C

Two real and two purely imaginary roots

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D

Neither real nor purely imaginary roots

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D Neither real nor purely imaginary roots If a quadratic equation has purely imaginary roots, then the coefficient of x must be equal to zero. Let p(x)=ax2+b with a,b of same sign and a,b ϵ R. Then, p[p(x)]=a(ax2+b)2+b p(x) has imaginary roots say ix. Then, ax2+b ϵ R and (ax2+b)2>0 ∴a(ax2+b)2+b≠0,∀ x ϵ R Thus, p[p(x)]≠0,∀ x ϵ R. Hence, p[p(x)]=0 has complex roots.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Geometric Representation and Trigonometric Form
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program