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Question: The set of values of a for which 1 lies between the roots of equation x<sup>2</sup> – ax – a + 3 = 0...

The set of values of a for which 1 lies between the roots of equation x2 – ax – a + 3 = 0 is-

A

(– , – 6)

B

(– , – 6]

C

(– , – 6) Č (2, )

D

(2, )

Answer

(2, )

Explanation

Solution

f(x) = x2 – ax – (a – 3) = 0

{(1) 6mu 6muD>0(2) 6mu 6muf(1)<0}\left\{ \begin{aligned} & (1)\mspace{6mu}\mspace{6mu} D > 0 \\ & (2)\mspace{6mu}\mspace{6mu} f(1) < 0 \end{aligned} \right\}

D > 0 Ž a2 + 4(a – 3) > 0

a2 + 4a – 12 > 0

(a + 6)(a – 2) > 0 ....(1)

f(1) < 0 Ž 1 – a – a + 3 < 0

Ž 2a > 4

Ž a > 2 ....(2)

Ž a > 2