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

A polynomial of 6th degree f(x) satisfies f(x)=f(2−x),∀xϵR, if f(x)=0 has 4 distinct and two equal roots, then sum of the roots of f(x)=0 is:

A
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
6
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
7
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 6In the functional relation replace x with x+1.We have,f(1+x)=f(1−x)This shows that the function is symmetric about x=1.There is one and only one double root. If the double root exists at any value x0 other than at x=1, then a double root will also exist at a value of 2−x0.Hence, the double root exists at x=1 Say two other roots are α and βf(α)=f(2−α)=0∴2−α is also a root.And similarly, 2−β is also a root.∴ the roots are 1,1,α,β,2−α,2−βHence, sum of the roots is 6

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
(a ± b ± c)²
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program