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0 votes
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in Mathematics by (67.9k points)

The values of p for which 6 lies between the roots of the equation x+ 2(p – 3)x + 9 = 0 is

(a) (-∞, -3/4)

(b)  (-∞, -3/4)

(c)  (-∞, 1)

(d) none of these

1 Answer

+1 vote
by (63.3k points)
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Best answer

Correct option (a) (-∞, -3/4)

Explanation:

D > 0

(– 2(p – 3))2 – 4.1.9 > 0

p– 6p > 0

p (p – 6) > 0

p < 0, p > 6 .....(1) 

a.ƒ(6) < 0

1.(36 + 12(p – 3) + 9)) < 0

12p + 9 < 0

P < -3/4  ...(2)

From (1) and (2)  P ∈ (-∞, -3/4)

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