The values of 'a' for which both roots of the equation (a +... | MATH - CONDITION FOR COMMON ROOTS, QUADRATIC EXPRESSIONS AND POSITION OF ROOTS | SolveeIt | Solveeit

Today, August 18

Question

The values of 'a' for which both roots of the equation (a + 1)x² –3ax + 4a = 0 are greater than unity:

A

$\left\lbrack \frac{- 16}{7},0 \right)$

B

$\left( \frac{- 1}{2},0 \right\rbrack$

C

$\left\lbrack \frac{- 16}{7}, - 1 \right)$

D

$\left( - 1,\frac{- 1}{2} \right)$

Answer

$\left\lbrack \frac{- 16}{7}, - 1 \right)$

Explanation

Solution

D ≥ 0 & $\frac{3a}{a + 1}$ > 2 & (a + 1) (2a + 1) > 0

⇒ $\frac{- 16}{7}$ ≤ a ≤ 0 & a < –1, a > 2 &

a < – 1, a > $\frac{- 1}{2}$ ⇒ a ∈ $\left\lbrack \frac{- 16}{7}, - 1 \right)$