Question

1) Find quad. polynomial whose zeros are
(2+√3) and (2-√2)​

Answer 1

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Given that,

Find quadratic polynomial whose zeroes are

(2 + √3) and (2 - √2).

Let,

• α = (2 + √3)
• ß = (2 - √2)

☯ α + ß = (2 + √3) + (2 - √3) = 2 + √3 + 2 - √3 = 4

☯ αß = (2 + √3)(2 - √3) = (2)² - (√3)² = 4 - 3 = 1

General form of quadratic polynomial is

↪ x² - (α + ß)x + αß = 0

Substitute the zeroes...

➡ x² - (4)x + (1) = 0

➡ x² - 4x + 1 = 0

$\underline{\boxed{\bf{\purple{∴ The\;Quadratic\;polynomial\;is\;“ \: x² - 4x + 1 = 0 \: "}}}}$

Step-by-step explanation:

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