Form a Quadratic Polynomial one of Whose Zeros is 2+√5 and the Sum of the Zeros is 4

Form a Quadratic Polynomial one of Whose Zeros is 2+√5 and the Sum of the Zeros is 4

Solution:

To form a quadratic polynomial with the given conditions, let's start by assuming the other zero is denoted as "z."

Since the sum of the zeros is 4, we have:

(2 + √5) + z = 4

We can solve this equation to find the value of z:

z = 4 - (2 + √5)

z = 4 - 2 - √5

z = 2 - √5

Now that we know the values of the two zeros, we can form the quadratic polynomial. The polynomial can be written as:

P(x) = (x - (2 + √5))(x - (2 - √5))

Expanding this expression, we get:

P(x) = (x - 2 - √5)(x - 2 + √5)

P(x) = (x - 2 - √5)(x - 2 + √5)

P(x) = (x - 2)² - (√5)²

P(x) = (x - 2)² - 5

P(x) = x² - 4x + 4 - 5

P(x) = x² - 4x - 1

Answer:

The Quadratic Polynomial, one of Whose Zeros is 2+√5 and the Sum of the Zeros is 4, is P(x) = x² - 4x - 1

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