Question

# If α and β are the roots of the equation a x2 + bx + c. find the equation whose roots are - α and - β.

A

ax2 + bx + c = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

ax2 - bx + c = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

cx2 + bx + a = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

cx2 - bx + a = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B ax2 - bx + c = 0 Solution: ax2 + bx + c roots are α and β α + β = −ba α . β = ca When roots are -α and -β -α -β = -(α + β) = ba (-α) × (-β) = αβ = ca Equation is x2 - (-α - β) × + (-α) (-β) = 0 x2 - (+ ca)n + ca = 0 ax2 - bx + c = 0 Alternatively If roots are equal in magnitude but opposite in sign we can replace x by (-x) in the given equation. a(−x)2 + b(-x) + c = 0 ax2 - bx + c = 0

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