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find the quadratic polynomial, the sum of whose zeros is 5/2 and their product is 1 .hence , find the zeros of the polynomial
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find the quadratic polynomial, the sum of whose zeros is 5/2 and their...
Quadratic polynomial = x^2 - ( sum of zeroes )x + product of zeroes
x^2 - 5 x/2 + 1 =0
2x^2 - 5x + 2 / 2 = 0 , 2x^2 - 5x + 2 = 0
Apply middle term split to find the zeroes
2x^2 - 5x + 2 = 0
2x^2 - 4x - x + 2 = 0
2x ( x - 2 ) - 1 ( x - 2 ) = 0
(2x - 1) ( x - 2 ) = 0
2x = 1
x = 1 / 2
Or
( x - 2 ) = 0
x = 2
x^2 - 5 x/2 + 1 =0
2x^2 - 5x + 2 / 2 = 0 , 2x^2 - 5x + 2 = 0
Apply middle term split to find the zeroes
2x^2 - 5x + 2 = 0
2x^2 - 4x - x + 2 = 0
2x ( x - 2 ) - 1 ( x - 2 ) = 0
(2x - 1) ( x - 2 ) = 0
2x = 1
x = 1 / 2
Or
( x - 2 ) = 0
x = 2
Community Answer
find the quadratic polynomial, the sum of whose zeros is 5/2 and their...
Solution:
Finding the Quadratic Polynomial
Let the two zeros of the quadratic polynomial be p and q, then:
p + q = 5/2
pq = 1
We know that sum of zeros of a quadratic polynomial is given by:
p + q = -b/a
where a and b are the coefficients of the quadratic polynomial ax^2 + bx + c.
Also, the product of the zeros of a quadratic polynomial is given by:
pq = c/a
where c is the constant term of the quadratic polynomial.
Using the above formulas, we can write:
p + q = -b/a = 5/2
pq = c/a = 1
Solving the first equation for b, we get:
b = -5a/2
Substituting this value of b in the second equation, we get:
pq = c/a = 1
Substituting the value of p + q from the first equation, we get:
p(5/2 - p) = 1
Simplifying the above equation, we get:
2p^2 - 5p + 2 = 0
Hence, the required quadratic polynomial is:
2x^2 - 5x + 2
Finding the Zeros of the Polynomial
To find the zeros of the polynomial, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/2a
Substituting the values of a, b, and c from the given quadratic polynomial, we get:
x = (5 ± √(25 - 16))/4
x = (5 ± 3)/4
Therefore, the zeros of the quadratic polynomial 2x^2 - 5x + 2 are:
x = 1/2 and x = 2
Finding the Quadratic Polynomial
Let the two zeros of the quadratic polynomial be p and q, then:
p + q = 5/2
pq = 1
We know that sum of zeros of a quadratic polynomial is given by:
p + q = -b/a
where a and b are the coefficients of the quadratic polynomial ax^2 + bx + c.
Also, the product of the zeros of a quadratic polynomial is given by:
pq = c/a
where c is the constant term of the quadratic polynomial.
Using the above formulas, we can write:
p + q = -b/a = 5/2
pq = c/a = 1
Solving the first equation for b, we get:
b = -5a/2
Substituting this value of b in the second equation, we get:
pq = c/a = 1
Substituting the value of p + q from the first equation, we get:
p(5/2 - p) = 1
Simplifying the above equation, we get:
2p^2 - 5p + 2 = 0
Hence, the required quadratic polynomial is:
2x^2 - 5x + 2
Finding the Zeros of the Polynomial
To find the zeros of the polynomial, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/2a
Substituting the values of a, b, and c from the given quadratic polynomial, we get:
x = (5 ± √(25 - 16))/4
x = (5 ± 3)/4
Therefore, the zeros of the quadratic polynomial 2x^2 - 5x + 2 are:
x = 1/2 and x = 2
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find the quadratic polynomial, the sum of whose zeros is 5/2 and their product is 1 .hence , find the zeros of the polynomial Related: Additional Questions Solution - Polynomials?
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find the quadratic polynomial, the sum of whose zeros is 5/2 and their product is 1 .hence , find the zeros of the polynomial Related: Additional Questions Solution - Polynomials? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about find the quadratic polynomial, the sum of whose zeros is 5/2 and their product is 1 .hence , find the zeros of the polynomial Related: Additional Questions Solution - Polynomials? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find the quadratic polynomial, the sum of whose zeros is 5/2 and their product is 1 .hence , find the zeros of the polynomial Related: Additional Questions Solution - Polynomials?.
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