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Find a quadratic polynomial, the sum of whose zeroes is 4 and one zero is 5.?
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Find a quadratic polynomial, the sum of whose zeroes is 4 and one zero...
Quadratic Polynomial with Sum of Zeroes and One Zero Given
To find a quadratic polynomial when the sum of the zeroes and one zero is given, we can use the properties of quadratic equations.
Given Information:
- Sum of zeroes = 4
- One zero = 5
Using the Sum of Zeroes Formula:
The sum of the zeroes of a quadratic polynomial in the form of ax^2 + bx + c is given by the formula:
Sum of zeroes = -b/a
Given Sum of Zeroes:
4 = -b/a
Using the Given Zero:
If one zero is 5, then the product of the zeroes is equal to the constant term divided by the leading coefficient.
Product of zeroes = c/a = 5
Solving for 'a' and 'b':
From the given information, we have:
4 = -b/a and c/a = 5
By substituting c/a = 5 into the product of zeroes formula, we get:
a = c/5
Substitute a = c/5 into the sum of zeroes formula:
4 = -b/(c/5)
4 = -5b/c
20 = -5b
b = -4
Now that we have found the values of 'a' and 'b', we can form the quadratic polynomial:
a = c/5
b = -4
c = 5
Therefore, the quadratic polynomial is:
5x^2 - 20x + 5.
To find a quadratic polynomial when the sum of the zeroes and one zero is given, we can use the properties of quadratic equations.
Given Information:
- Sum of zeroes = 4
- One zero = 5
Using the Sum of Zeroes Formula:
The sum of the zeroes of a quadratic polynomial in the form of ax^2 + bx + c is given by the formula:
Sum of zeroes = -b/a
Given Sum of Zeroes:
4 = -b/a
Using the Given Zero:
If one zero is 5, then the product of the zeroes is equal to the constant term divided by the leading coefficient.
Product of zeroes = c/a = 5
Solving for 'a' and 'b':
From the given information, we have:
4 = -b/a and c/a = 5
By substituting c/a = 5 into the product of zeroes formula, we get:
a = c/5
Substitute a = c/5 into the sum of zeroes formula:
4 = -b/(c/5)
4 = -5b/c
20 = -5b
b = -4
Now that we have found the values of 'a' and 'b', we can form the quadratic polynomial:
a = c/5
b = -4
c = 5
Therefore, the quadratic polynomial is:
5x^2 - 20x + 5.
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Find a quadratic polynomial, the sum of whose zeroes is 4 and one zero is 5.?
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Find a quadratic polynomial, the sum of whose zeroes is 4 and one zero is 5.? 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 a quadratic polynomial, the sum of whose zeroes is 4 and one zero is 5.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a quadratic polynomial, the sum of whose zeroes is 4 and one zero is 5.?.
Find a quadratic polynomial, the sum of whose zeroes is 4 and one zero is 5.? 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 a quadratic polynomial, the sum of whose zeroes is 4 and one zero is 5.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a quadratic polynomial, the sum of whose zeroes is 4 and one zero is 5.?.
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