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

If α and β are the zeroes of the quadratic polynomial 2S28S+4, then the value of αβ+βα+2(1α+1β)+3αβ is ___.

A
8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
16
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 16
Given, f(S)=2S28S+4.
Let α and β be its zeroes.
α+β=82=4and αβ=42=2
Now,
αβ+βα+2(1α+1β)+3αβ

=α2+β2αβ+2(α+βαβ)+3αβ

=(α+β)22αβαβ+2(α+βαβ)+3αβ

[(α+β)2=α2+β2+2αβ]

=(4)22×22+2(42)+3×2

= 6 + 4 + 6 = 16

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Relationship Between Zeroes and Coefficients of a Quadratic Polynomial
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon