UPSC Exam  >  UPSC Questions  >  If the ratio of the roots of the Equation 4x2... Start Learning for Free
If the ratio of the roots of the Equation 4x2
-6x+p=0 is 1:2 then the value of p
is:
(a) 1
(b) 2
(c) -2
(d) -1?
Most Upvoted Answer
If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the ...
Solution:

Given: 4x^2 - 6x + p = 0

Ratio of roots: 1:2

Let the roots be α and 2α

Sum of roots: α + 2α = 3α = -(-6)/4 = 3/2

Product of roots: α * 2α = 2α^2 = p/4

By sum and product of roots formula:
- Sum of roots = -b/a = 3/2
- Product of roots = c/a = p/4

Substitute the values in the equations:
- -b/a = 3/2 ⟹ -(-6)/4 = 3/2 ⟹ 6/4 = 3/2 ⟹ 3 = 3 (True)
- c/a = p/4 ⟹ p/4 = 3/2 ⟹ p = 4 * 3/2 ⟹ p = 6
Therefore, the value of p is 6.
So, the correct answer is (b) 6.
Explore Courses for UPSC exam

Top Courses for UPSC

If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1?
Question Description
If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1?.
Solutions for If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1? in English & in Hindi are available as part of our courses for UPSC. Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1? defined & explained in the simplest way possible. Besides giving the explanation of If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1?, a detailed solution for If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1? has been provided alongside types of If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1? theory, EduRev gives you an ample number of questions to practice If the ratio of the roots of the Equation 4x2 -6x+p=0 is 1:2 then the value of p is: (a) 1 (b) 2 (c) -2 (d) -1? tests, examples and also practice UPSC tests.
Explore Courses for UPSC exam

Top Courses for UPSC

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev