Relation between Roots and Coefficients for Quadratic
If α, β are t...
Question
If α,β are the roots of 3x2+7x+5=0, then the value of (13α+7)3+(13β+7)3 is
A
6723375
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
283375
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
−6723375
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
−283375
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B283375
α,β are the roots of 3x2+7x+5=0 ⇒3α2+7α+5=0 and 3β2+7β+5=0 ⇒13α+7=−α5 and 13β+7=−β5 ∴(13α+7)3+(13β+7)3=(−α5)3+(−β5)3 =−1125(α3+β3) =−1125(α+β)(α2−αβ+β2) =−1125(α+β)[(α+β)2−3αβ] =−1125(−73)[499−3×53] =283375