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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?
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If the ratio of the roots of the equation 4x²-6x+p=0 is 1:2 then the v...
Ratio of Roots of the Equation
The ratio of the roots of a quadratic equation ax² + bx + c = 0 is given by (-b ± √(b²-4ac))/2a. In this case, the roots of the equation 4x² - 6x + p = 0 are in the ratio 1:2.
Using the Ratio of Roots Formula
Let the roots of the equation be x and 2x. By the sum and product of roots formula, the sum of the roots is -(-6)/4 = 3/2 and the product of the roots is p/4. Therefore, x + 2x = 3/2 and x(2x) = p/4.
Solving for p
From x + 2x = 3/2, we get 3x = 3/2, which gives x = 1/2. Substituting x = 1/2 in x(2x) = p/4, we get 1/2 * 2 * 1/2 = p/4, which simplifies to p/4 = 1/4. Thus, p = 1.
Therefore, the value of p in the equation 4x² - 6x + p = 0 such that the roots are in the ratio 1:2 is p = 1.
The ratio of the roots of a quadratic equation ax² + bx + c = 0 is given by (-b ± √(b²-4ac))/2a. In this case, the roots of the equation 4x² - 6x + p = 0 are in the ratio 1:2.
Using the Ratio of Roots Formula
Let the roots of the equation be x and 2x. By the sum and product of roots formula, the sum of the roots is -(-6)/4 = 3/2 and the product of the roots is p/4. Therefore, x + 2x = 3/2 and x(2x) = p/4.
Solving for p
From x + 2x = 3/2, we get 3x = 3/2, which gives x = 1/2. Substituting x = 1/2 in x(2x) = p/4, we get 1/2 * 2 * 1/2 = p/4, which simplifies to p/4 = 1/4. Thus, p = 1.
Therefore, the value of p in the equation 4x² - 6x + p = 0 such that the roots are in the ratio 1:2 is p = 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?
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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? 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? 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?.
If the ratio of the roots of the equation 4x²-6x+p=0 is 1:2 then the value of p is? 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? 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?.
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