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

By Mohit Uniyal|Updated : May 22nd, 2023

Form a quadratic polynomial one of whose zeros is 2+√5 and the sum of the zeros is 4

In the question, we are provided with one of the zeros and sum of those zeros. We will use the basic mathematical expression with substituion to find the value of the other root.

On finding the root, we will use the given equation to form quadratic polynomial using the zeros: P(x) = (x - α)(x - β)

On Substituting the values of α and β and expanding the expression, we will get the desired result.

## 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

## 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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