Question

Find the quadratic polynomial whose zero are 2+✓3 and 2-✓3

Answer 1

Quadratic Polynomial :

K[x²-(sum of zeroes)+(product of zeroes)]

Sum of zeroes = 2+√3+2-√3 = 4

Product of Zeroes = (2+√3)(2-√3) = (2)²-(√3)² = 1

So the quadratic polynomial =

k[x²-4x+1]

Answer 2

♊♊YOUR ANSWERS♍♍

✍x² - 4x + 1

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EXPLANATION —

Given—

Zeros of polynomial are α= 2+√3 & β=2-√3

To find - the polynomial equation

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Sum of Zeroes α + β = 2+√3+2-√3 = 4

Product of Zeros αβ = (2+√3)(2-√3) = 2² - 3 =1

General form Polynomial equation

x² - (α+β)x + αβ

Now substituting the values we get the required polynomial

⇒x² - 4x + 1

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