Match the following:
Column I | Column II |
(i) Let f(x) = (a2 + a + 2)x2 – (a + 4)x – 7. If unity lies between roots of f(x) = 0, then possible integral value of a is/are | [A] 1 |
(ii) Possible integral value of x satisfying 1 < < 2 is/are | [B] 2 |
(iii) Value of x for which (log5x)2 + 1og5x(5/x) = 1 is/are | [C] 4 |
(iv) Value of 4log18() + log18729 is | [D] 5 |
[E] 6 |
Text Solution
Verified by Experts(i) [A]; (ii) [B]; (iii) [A]; (iv) [B]
Ans.
(i) [A], [B]
(ii) [B], [C], [D]
(iii) [A], [D]
(iv) [B]
Sol. (i) f(1) < 0 { coefficient of x 2 > 0}
a 2 – 9 < 0
– 3 < a < 3
(ii) x 2 + 1 < 3x 2 – 7x + 8 < 2x 2 + 2
⇒ x 2 + 1 < 3x 2 – 7x + 8
2x 2 – 7x + 7 > 0
which is true always as D < 0
∴ x ∈ R
Also x 2 – 7x + 6 < 0
1 < x < 6
(iii) Let 1og 5 x = y
(log 5 x) 2 + log 5x 5 – log 5x x = 1
⇒ 
= 1
⇒ y 2 + 
= 1
⇒ y 2 – 1 + 
= 0
⇒ (y – 1) 
⇒ y = 1 or (y + 1) 2 = 1
⇒ y = 0 or – 2
⇒ x = 5 or x = 1 or x = 
(iv) 2log 18 2 + 
. 
= 
= 
= 2
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems