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If α , β are the zeroes of f(x) = px2 – 2x + 3p and α + β = αβ then the value of p is:
- a)1/3
- b)-2/3
- c)2/3
- d)-1/3
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If α , β are the zeroes of f(x) = px2– 2x + 3p and ...
The given polynomial is
Also, α and β are the zeros of p(x).
and α + β = α × β
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If α , β are the zeroes of f(x) = px2– 2x + 3p and ...
Given: Zeroes of f(x) = px2 2x 3p are
To find: The value of p
Solution:
1. Finding the quadratic equation using the given zeroes
We know that the quadratic equation with zeroes and is given by:
f(x) = a(x- )(x- )
Substituting the given values of and in the above equation, we get:
f(x) = a(x- )(x- )
f(x) = a(x- )(x- )
To find the value of 'a', we can use the given equation:
f(x) = px2 2x 3p
Substituting the above equation in the quadratic equation, we get:
px2 2x 3p = a(x- )(x- )
2. Simplifying the equation
Expanding the right-hand side of the above equation, we get:
px2 2x 3p = a(x2 - x - x + )
px2 2x 3p = a(x2 - 2x + )
px2 2x 3p = ax2 - 2ax + a
Comparing the coefficients of x2 on both sides, we get:
p = a
Comparing the constant terms on both sides, we get:
3p = a
Substituting the value of a in terms of p in the second equation, we get:
3p = p
3 =
p =
p =
3. Checking the answer
Substituting the value of p in the given equation, we get:
f(x) = px2 2x 3p
f(x) = ( )x2 2x 3( )
f(x) = ( )(x2 - 2x - 3)
f(x) = ( )(x - 3)(x + 1)
The zeroes of the above equation are and , which are the given zeroes of the function.
Therefore, the value of p is 2/3, which is option (c).
To find: The value of p
Solution:
1. Finding the quadratic equation using the given zeroes
We know that the quadratic equation with zeroes and is given by:
f(x) = a(x- )(x- )
Substituting the given values of and in the above equation, we get:
f(x) = a(x- )(x- )
f(x) = a(x- )(x- )
To find the value of 'a', we can use the given equation:
f(x) = px2 2x 3p
Substituting the above equation in the quadratic equation, we get:
px2 2x 3p = a(x- )(x- )
2. Simplifying the equation
Expanding the right-hand side of the above equation, we get:
px2 2x 3p = a(x2 - x - x + )
px2 2x 3p = a(x2 - 2x + )
px2 2x 3p = ax2 - 2ax + a
Comparing the coefficients of x2 on both sides, we get:
p = a
Comparing the constant terms on both sides, we get:
3p = a
Substituting the value of a in terms of p in the second equation, we get:
3p = p
3 =
p =
p =
3. Checking the answer
Substituting the value of p in the given equation, we get:
f(x) = px2 2x 3p
f(x) = ( )x2 2x 3( )
f(x) = ( )(x2 - 2x - 3)
f(x) = ( )(x - 3)(x + 1)
The zeroes of the above equation are and , which are the given zeroes of the function.
Therefore, the value of p is 2/3, which is option (c).
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If α , β are the zeroes of f(x) = px2– 2x + 3p and α + β = αβ then the value of p is:a)1/3b)-2/3c)2/3d)-1/3Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If α , β are the zeroes of f(x) = px2– 2x + 3p and α + β = αβ then the value of p is:a)1/3b)-2/3c)2/3d)-1/3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α , β are the zeroes of f(x) = px2– 2x + 3p and α + β = αβ then the value of p is:a)1/3b)-2/3c)2/3d)-1/3Correct answer is option 'C'. Can you explain this answer?.
If α , β are the zeroes of f(x) = px2– 2x + 3p and α + β = αβ then the value of p is:a)1/3b)-2/3c)2/3d)-1/3Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If α , β are the zeroes of f(x) = px2– 2x + 3p and α + β = αβ then the value of p is:a)1/3b)-2/3c)2/3d)-1/3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α , β are the zeroes of f(x) = px2– 2x + 3p and α + β = αβ then the value of p is:a)1/3b)-2/3c)2/3d)-1/3Correct answer is option 'C'. Can you explain this answer?.
Solutions for If α , β are the zeroes of f(x) = px2– 2x + 3p and α + β = αβ then the value of p is:a)1/3b)-2/3c)2/3d)-1/3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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