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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:?
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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 equation is: 4x^2 - 6xp = 0
Let the roots be a and 2a, where a/2a = 1/2
So, a = x and 2a = 2x
Sum of roots = a + 2a = 3a = x + 2x = 3x
Product of roots = a × 2a = 2a^2 = 2x^2
By sum and product of roots formula, we have:
Sum of roots = -b/a = 3x
Product of roots = c/a = 2x^2
On comparing with the given equation, we get:
-b/a = 3x => -(-6p)/4 = 3x => 3p/2 = 3x => p = 2x
c/a = 2x^2 => -6p/4 = 2x^2 => -3p/2 = x^2 => p = -2x^2/3
Equating both values of p, we get:
2x = -2x^2/3 => 6x = -2x^2 => x^2 = -3x
As x ≠ 0, we can divide by x on both sides, we get:
x = -3
Therefore, the roots are -3 and -6
Hence, the value of p = -2x^2/3 = -2(-3)^2/3 = -2 × 3/3 = -2
Therefore, the value of p is -2.
Given equation is: 4x^2 - 6xp = 0
Let the roots be a and 2a, where a/2a = 1/2
So, a = x and 2a = 2x
Sum of roots = a + 2a = 3a = x + 2x = 3x
Product of roots = a × 2a = 2a^2 = 2x^2
By sum and product of roots formula, we have:
Sum of roots = -b/a = 3x
Product of roots = c/a = 2x^2
On comparing with the given equation, we get:
-b/a = 3x => -(-6p)/4 = 3x => 3p/2 = 3x => p = 2x
c/a = 2x^2 => -6p/4 = 2x^2 => -3p/2 = x^2 => p = -2x^2/3
Equating both values of p, we get:
2x = -2x^2/3 => 6x = -2x^2 => x^2 = -3x
As x ≠ 0, we can divide by x on both sides, we get:
x = -3
Therefore, the roots are -3 and -6
Hence, the value of p = -2x^2/3 = -2(-3)^2/3 = -2 × 3/3 = -2
Therefore, the value of p is -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:?
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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:? 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:? 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:?.
If the ratio of the roots of the equation 4x 2 -6x p=0 is 1:2 then the value of p is:? 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:? 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:?.
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