Find a quadratic polynomial whose zeroes are4-√5/3 and 4+√5/3 .
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Zeroes are 4 - √5/3 and 4 + √5/3
Sum of the zeroes = 4 - √5/3 + 4 + √5/3
= 4 + 4 + √5 - √5/3 = 8 + 0/3 = 8/3
i. e., alpha + beta = 8/3
Product of zeroes = 4 - √5/3 × 4 + √5/3
= (4 - √5)(4 + √5)/3 × 3
= 4² - (√5)²/9 = 16 - 5 / 9 = 11/9
Then the polynomial is of the form
x² - (alpha + beta ) × x + (alpha × beta) = 0
x² - 8/3 × x + 11/9 = 0
x² - 8x /3 + 11/9 = 0
9x² - 24x² + 11/9 = 0
9x² - 24x² + 11
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