Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Consider the quadratic equation, (log 10 8)x 2 – (log 10 5)x = 2(log 2 10) –1 – x. Which of the following quantities are irrational.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(c,d)(log 10 8)x 2 – (log 10 5)x + x – 2log 10 2 = 0
sum of roots = 
= 
rational
Product of roots = 
sum of cofficient = log 10 8 – log 10 5 + 1 – log 10 4 = log 10 
= log 10 4 = irrational
Dirscriminant = (log 10 2) 2 – 4log 10 8(–2log 10 2) = (log 10 2) 2 + 24(log 10 2) 2
= 25(log 10 2) 2 = (5log 10 2) 2
irrational
──────────────────────────────────────────────────────────────────────────────────────────
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
Match the set P in column one with its super set Q in column II
Column – Ι (set P) Column – ΙΙ (set…
If ≤ 4, then the least and the highest values of 4x 2 are:
If ≥ 1 and is an odd integer then number of possible values of α is
If log a b = 2; log b c = 2 and log 3 c = 3 + log 3 a then (a + b + c) equals
The sum of the solutions of the equation 9 x – 6 · 3 x + 8 = 0 is
The expression: reduces to