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Answers:

We know that,

The standard form of quadratic polynomial,

=> x² - (sum of zeroes)x + (product of zeroes)

a) 1/4, - 1

=> x² - (1/4)x + (-1)

=> x² - (1/4)x - 1

=> 4x² - x - 4

(b) √2,1/3

=> x² - (√2)x + 1/3

=> x² - √2x + 1/3

=> 3x² - 3√2 + 1

(c) 0,√5

=> x² - (0)x + √5

=> x² - ox + √5

=> x² + √5

(d) 1,1

=> x² - (1)x + 1

=> x² - x + 1

(e) -1/4,1/4

=> x² - (-1/4)x + (1)4)

=> x² + 1/4 x + 1/4

=> 4x² + x + 1

(f) 4,1

=> x² - (4)x + 1

=> x² - 4x + 1

Therefore, the required polynomials are:

a) 4x² - x - 4 b) 3x² - 3√2 + 1 c) x² + √5

d) x² - x + 1 e) 4x² + x + 1 f) x² - 4x + 1