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

By BYJU'S Exam Prep

Updated on: October 17th, 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.

Table of content ## 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 GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com