NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice
If one root of the equation x 2 + p x + q = 0 is the square of the other, then
Options
- Ap 3 + q 2 − q ( 3 p + 1 ) = 0
- Bp 3 + q 2 + q ( 1 + 3 p ) = 0
- Cp 3 + q 2 + q ( 3 p − 1 ) = 0
- Dp 3 + q 2 + q ( 1 − 3 p ) = 0
Correct answer
D. p 3 + q 2 + q ( 1 − 3 p ) = 0
Step-by-step solution
x 2 + p x + q = 0 Let, α , α 2 are the roots of the given equation. ⇒ α + α 2 = - p and α · α 2 = q ⇒ α 3 = q ∵ α + α 2 = - p ⇒ α + α 2 3 = - p 3 ⇒ α 6 + α 3 + 3 α . α 2 α + α 2 = - p 3 ⇒ q 2 + q + 3 α 3 α + α 2 = - p 3 ⇒ q 2 + q + 3 q - p = - p 3 ⇒ p 3 + q 2 + q - 3 p q = 0 ⇒ p 3 + q 2 + q 1 - 3 p = 0