Question

The quadratic polynomial in 'x' when zeroes are 2+root5 and 2-root5 is
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Answer 1

Answer:

we use x²-(sum of its zeroes )x+ product of its zeroes

X²-(2+√5+2-√5)x+(2+√5)(2-√5)

x²-(4)x+{(2)²-(√5)²}. ➡️using a²-b²=(a +b)(a-b)

x²-4x+(-1)

answer x²-4x-1

Answer 2

$\huge\underline\mathfrak{Answer-}$

$\huge{\boxed{\rm{\red{x^2-4x-1}}}}$

$\huge\underline\mathfrak{Explanation-}$

Given roots :

• 2 + √5
• 2 - √5

To find :

• Quadratic polynomial

Solution :

★ Sum of given zeroes = 2 + $\cancel{\sqrt{5}}$ + 2 - $\cancel{\sqrt{5}}$

: $\implies$ Sum of zeroes = 4

★ Product of zeroes = (2 + √5)(2 - √5)

By using (a+b)(a-b) = a² - b²

: $\implies$ Product of zeroes = (2)² - (√5)²

: $\implies$ Product of zeroes = 4 - 5

: $\implies$ Product of zeroes = -1

Now,

Formation of quadratic polynomial = x² - Sx + P

Where, S refers to sum of zeroes and P refers to product of zeroes.

Putting the values,

: $\implies$ x² - 4x + (-1)

We get the Quadratic polynomial as :

$\huge{\boxed{\rm{\red{x^2-4x-1}}}}$