Question

Form a quadriate polynomial whose zero'es are 2 + 13 and 2 - V3

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Answer 1

Step-by-step explanation:

Sum of zeroes=2+√3+2-√3=4

Product of zeroes=(2+√3)(2-√3)=(2)^2-(√3)^2

=1

Polynomial

x^2-(Sum of zeroes)x+(Product of zeroes)

x^2-4x+1

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Answer 2

Answer:

x² - 4x + 1

Step-by-step explanation:

It is given that 2 + √3 and 2 - √3 are the zeroes of the required polynomial.

Let the two zeroes be α and β of the required polynomial.

∴ α = 2 + √3, β = 2 - √3

_____________________________

Now,

• Sum of zeroes = α + β

→ (2 + √3) + (2 - √3)

→ 2 + √3 + 2 - √3

→ 2 + 2

→ 4

• Product of zeroes = αβ

→ (2 + √3)(2 - √3)

• Identity : (a + b)(a - b) = a² - b²

Here, a = 2, b = √3

→ (2)² - (√3)²

→ 4 - 3

→ 1

_____________________________

The required polynomial is :

→ p(x) = k [ x² - (α + β)x + αβ ]

• Putting known values.

→ p(x) = k [ x² - (4)x + (1) ]

→ p(x) = k [x² - 4x + 1]

• Putting k = 1.

→ p(x) = x² - 4x + 1