Class 10 Exam > Class 10 Questions > 1) Given that x – √5 is a factor of the polyn...
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1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5,
find all the zeroes of the polynomial.
(x -3) and (x + √5)?
find all the zeroes of the polynomial.
(x -3) and (x + √5)?
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1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + ...
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1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + ...
Zeroes of the Polynomial
Given:
The polynomial is x^3 – 3√5 x^2 – 5x + 15√5.
One of the factors is x – √5.
Finding other factors:
To find the other factors, we can perform polynomial division.
Dividing x^3 – 3√5 x^2 – 5x + 15√5 by x – √5, we get x^2 - 3√5x + 3√5.
Finding the remaining factor:
Now, we have x^2 - 3√5x + 3√5 as the quotient.
To find the remaining factor, we can factorize this quadratic equation.
Factoring the quadratic equation:
The quadratic equation x^2 - 3√5x + 3√5 can be factored as (x - 3)(x + √5).
Zeroes of the Polynomial:
Therefore, the zeroes of the polynomial x^3 – 3√5 x^2 – 5x + 15√5 are x = 3, x = -√5, and x = √5.
Conclusion:
By factoring the given polynomial and using the given factor, we have found all the zeroes of the polynomial.
Given:
The polynomial is x^3 – 3√5 x^2 – 5x + 15√5.
One of the factors is x – √5.
Finding other factors:
To find the other factors, we can perform polynomial division.
Dividing x^3 – 3√5 x^2 – 5x + 15√5 by x – √5, we get x^2 - 3√5x + 3√5.
Finding the remaining factor:
Now, we have x^2 - 3√5x + 3√5 as the quotient.
To find the remaining factor, we can factorize this quadratic equation.
Factoring the quadratic equation:
The quadratic equation x^2 - 3√5x + 3√5 can be factored as (x - 3)(x + √5).
Zeroes of the Polynomial:
Therefore, the zeroes of the polynomial x^3 – 3√5 x^2 – 5x + 15√5 are x = 3, x = -√5, and x = √5.
Conclusion:
By factoring the given polynomial and using the given factor, we have found all the zeroes of the polynomial.
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1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.(x -3) and (x + √5)?
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1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.(x -3) and (x + √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 1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.(x -3) and (x + √5)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.(x -3) and (x + √5)?.
1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.(x -3) and (x + √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 1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.(x -3) and (x + √5)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1) Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.(x -3) and (x + √5)?.
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