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If alpha and beta the zeroes of the polynomial 4x² 4x 1 , then form a quadratic polynomial whose zeroes are 2alpha and 2 beta?
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If alpha and beta the zeroes of the polynomial 4x² 4x 1 , then form a ...
Forming a Quadratic Polynomial with Zeroes 2α and 2β
Finding the Zeroes of the Given Polynomial
To find the zeroes of the polynomial 4x² + 4x + 1, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Plugging in the values of a, b, and c from our polynomial, we get:
x = (-4 ± √(16 - 16)) / 8
Simplifying, we get:
x = (-4 ± 1) / 8
Which gives us the two zeroes: α = -1/2 and β = -1/2.
Finding the Zeroes of the Desired Quadratic Polynomial
We want to find a quadratic polynomial with zeroes 2α and 2β. To do this, we can use the fact that if a polynomial has zeroes α and β, then it can be written as:
P(x) = (x - α)(x - β)
Thus, a quadratic polynomial with zeroes 2α and 2β can be written as:
Q(x) = (x - 2α)(x - 2β)
Plugging in the Values of α and β
We already know the values of α and β from the given polynomial. Plugging these values into the expression for Q(x), we get:
Q(x) = (x - 2(-1/2))(x - 2(-1/2))
Simplifying, we get:
Q(x) = (x + 1)(x + 1)
Which is the desired quadratic polynomial.
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If alpha and beta the zeroes of the polynomial 4x² 4x 1 , then form a quadratic polynomial whose zeroes are 2alpha and 2 beta? 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 alpha and beta the zeroes of the polynomial 4x² 4x 1 , then form a quadratic polynomial whose zeroes are 2alpha and 2 beta? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta the zeroes of the polynomial 4x² 4x 1 , then form a quadratic polynomial whose zeroes are 2alpha and 2 beta?.
If alpha and beta the zeroes of the polynomial 4x² 4x 1 , then form a quadratic polynomial whose zeroes are 2alpha and 2 beta? 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 alpha and beta the zeroes of the polynomial 4x² 4x 1 , then form a quadratic polynomial whose zeroes are 2alpha and 2 beta? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta the zeroes of the polynomial 4x² 4x 1 , then form a quadratic polynomial whose zeroes are 2alpha and 2 beta?.
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