Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes, respectively.

1/4, -1

Dear Student

From the formulas of sum and product of zeroes, we know,
Sum of zeroes = α + β
Product of zeroes = αβ

Given,

Sum of zeroes = 1/4
Product of zeroes = -1

Therefore, if α and β are zeroes of any quadratic polynomial, then the polynomial can be written as:-
x^2– (α + β)x + αβ

x^2– (1/4)x + (-1)

4x^2– x – 4

Thus,
4x^2– x – 4 is the required quadratic polynomial.

Thanks