If 1 ∈ α , β where α , β are the roots of the equation x 2 - a x + 1 + 3 = 0, then

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Question: Answered & Verified by Expert

If

1 \in (α, β)

where

α, β

are the roots of the equation

x^{2} - a (x + 1) + 3 = 0,

then

MathematicsQuadratic EquationJEE Main

Options:

A $a > 2$
B $a < - 6$ or $a > 2$
C $- 6 < a < 2$
D $a < 2$

Solution:

1423 Upvotes Verified Answer

The correct answer is:

a > 2

Coefficient of

x^{2}

is

+ v e

, so parabola is opening upward.

1

lies between the roots

\Rightarrow f (1) < 0

\Rightarrow 1 - a \cdot 2 + 3 < 0

\Rightarrow 2 a > 4 \Rightarrow a > 2

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