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Find a quadratic polynomial, the sum and product of whose zeroes are 0 and -√2 respectively.?
Most Upvoted Answer
Find a quadratic polynomial, the sum and product of whose zeroes are 0...
Solution:
Given, sum of zeroes = 0 and product of zeroes = -√2
Let the quadratic polynomial be ax² + bx + c
Sum of zeroes = -b/a = 0
=> b = 0
Product of zeroes = c/a = -√2
=> c = -a√2
Therefore, the quadratic polynomial is ax² - a√2x
Let's assume a = 1 for simplicity
So, the quadratic polynomial is x² - √2x
Verification:
Sum of zeroes = -b/a = 0
Product of zeroes = c/a = -√2
The zeroes of the polynomial can be obtained by equating it to zero and solving for x
x² - √2x = 0
x(x - √2) = 0
x = 0 or x = √2
Sum of zeroes = 0 + √2 = √2
Product of zeroes = 0 * √2 = 0
Therefore, the quadratic polynomial x² - √2x has zeroes 0 and √2, with sum 0 and product -√2.
Given, sum of zeroes = 0 and product of zeroes = -√2
Let the quadratic polynomial be ax² + bx + c
Sum of zeroes = -b/a = 0
=> b = 0
Product of zeroes = c/a = -√2
=> c = -a√2
Therefore, the quadratic polynomial is ax² - a√2x
Let's assume a = 1 for simplicity
So, the quadratic polynomial is x² - √2x
Verification:
Sum of zeroes = -b/a = 0
Product of zeroes = c/a = -√2
The zeroes of the polynomial can be obtained by equating it to zero and solving for x
x² - √2x = 0
x(x - √2) = 0
x = 0 or x = √2
Sum of zeroes = 0 + √2 = √2
Product of zeroes = 0 * √2 = 0
Therefore, the quadratic polynomial x² - √2x has zeroes 0 and √2, with sum 0 and product -√2.
Community Answer
Find a quadratic polynomial, the sum and product of whose zeroes are 0...
We know
sum of zeros = 0
product of zeros = -√2
we know a formula
x2-(sum of zeros) x + ( product of zeros)
x2 -(0)x + (-√2)
x2 - √2 is a quadratic polynomial
sum of zeros = 0
product of zeros = -√2
we know a formula
x2-(sum of zeros) x + ( product of zeros)
x2 -(0)x + (-√2)
x2 - √2 is a quadratic polynomial
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Find a quadratic polynomial, the sum and product of whose zeroes are 0 and -√2 respectively.?
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Find a quadratic polynomial, the sum and product of whose zeroes are 0 and -√2 respectively.? 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 and product of whose zeroes are 0 and -√2 respectively.? 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 and product of whose zeroes are 0 and -√2 respectively.?.
Find a quadratic polynomial, the sum and product of whose zeroes are 0 and -√2 respectively.? 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 and product of whose zeroes are 0 and -√2 respectively.? 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 and product of whose zeroes are 0 and -√2 respectively.?.
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