If the sum of two of the roots of x4−5x3−3x2+15x=0 is zero, then the roots are
A
0,5,±√3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
0,5,±√2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
0,5,±√5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
0,5,±√6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A0,5,±√3 Let α,β,γ,δ be the roots of x4−5x3−3x2+15=0 Such that α+β=0 S1=α+β+γ+δ=5⇒γ+δ=5S3=αβ+αγ+αδ+βγ+β+γδ=−15⇒(α+β)γ+(α+β)δ+αβ+γδ=−15⇒αβ+γδ=−15 Now from option only option A satisfies all conditions