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If the ratio of the roots of the equation 4x 2 -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 4x 2 -6x p=0 is 1:2 then the...
Solution:
Given, the equation is 4x^2 - 6xp = 0
Let the roots of the equation be a and b such that a:b = 1:2
Ratio of roots of a quadratic equation
The ratio of the roots of the quadratic equation ax^2 + bx + c = 0 is (-b ± √(b^2 - 4ac))/2a
Therefore, a:b = (-(-6p) ± √((-6p)^2 - 4(4)(0)))/2(4)
Simplifying, we get 1:2 = (3p ± √(9p^2))/4
Squaring both sides, we get (1/4) = (9p^2)/16
Solving the above equation, we get p = ±2/3
But we need to find the value of p, which satisfies the given equation.
Substituting p = 2/3 in the given equation, we get 4x^2 - 4x = 0
Solving the above equation, we get x = 0, 1
Therefore, the roots of the equation are 0 and 1, and their ratio is 0:1, which is not equal to 1:2.
Substituting p = -2/3 in the given equation, we get 4x^2 + 4x = 0
Solving the above equation, we get x = 0, -1/4
Therefore, the roots of the equation are 0 and -1/4, and their ratio is 0:-1/4, which is equal to 1:2.
Hence, the value of p is -2/3.
Answer: c) -2
Given, the equation is 4x^2 - 6xp = 0
Let the roots of the equation be a and b such that a:b = 1:2
Ratio of roots of a quadratic equation
The ratio of the roots of the quadratic equation ax^2 + bx + c = 0 is (-b ± √(b^2 - 4ac))/2a
Therefore, a:b = (-(-6p) ± √((-6p)^2 - 4(4)(0)))/2(4)
Simplifying, we get 1:2 = (3p ± √(9p^2))/4
Squaring both sides, we get (1/4) = (9p^2)/16
Solving the above equation, we get p = ±2/3
But we need to find the value of p, which satisfies the given equation.
Substituting p = 2/3 in the given equation, we get 4x^2 - 4x = 0
Solving the above equation, we get x = 0, 1
Therefore, the roots of the equation are 0 and 1, and their ratio is 0:1, which is not equal to 1:2.
Substituting p = -2/3 in the given equation, we get 4x^2 + 4x = 0
Solving the above equation, we get x = 0, -1/4
Therefore, the roots of the equation are 0 and -1/4, and their ratio is 0:-1/4, which is equal to 1:2.
Hence, the value of p is -2/3.
Answer: c) -2
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If the ratio of the roots of the equation 4x 2 -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 4x 2 -6x p=0 is 1:2 then the value of p is: a) 1 b) 2 c) -2 d) -1? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the ratio of the roots of the equation 4x 2 -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 CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the ratio of the roots of the equation 4x 2 -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 4x 2 -6x p=0 is 1:2 then the value of p is: a) 1 b) 2 c) -2 d) -1? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the ratio of the roots of the equation 4x 2 -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 CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the ratio of the roots of the equation 4x 2 -6x p=0 is 1:2 then the value of p is: a) 1 b) 2 c) -2 d) -1?.
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