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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?
-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.
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.
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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?
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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?.
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?.
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