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

# If α,β be the roots of the equation ax2+bx+c=0. Let Sn=αn+βn, for n≥1 If Δ=∣∣ ∣∣31+S11+S21+S11+S21+S31+S21+S31+S4∣∣ ∣∣, then Δ is equal to

A
s2(b24ac)a4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(a+b+c)2(b24ac)a4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
b24aca4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(a+b+c)24
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B (a+b+c)2(b2−4ac)a4We have α,β are the roots of ax2+bx+c=0, then α+β=−ba, αβ=ca ∴Sn=αn+βn ∴Δ=∣∣ ∣∣31+S11+S21+S11+S21+S31+S21+S31+S4∣∣ ∣∣ =∣∣ ∣ ∣∣31+α+β1+α2+β21+α+β1+α2+β21+α3+β31+α2+β21+α3+β31+α4+β4∣∣ ∣ ∣∣ =∣∣ ∣∣1111αβ1α2β2∣∣ ∣∣×∣∣ ∣∣1111αβ1α2β2∣∣ ∣∣ =∣∣ ∣∣1111αβ1α2β2∣∣ ∣∣2 ={αβ−(α+β)+1}2{(α+β)2−4αβ}=(ca+ba+1)2(b2a2−4ca)=(a+b+c)2(b2−4ac)a4

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Properties
MATHEMATICS
Watch in App
Join BYJU'S Learning Program