Question

find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively 1 upon 4 and -1​

Answer 1

Sum of zeroes = 1/4 = -b/a

$\alpha + \beta$

Product of zeroes = -1 = c/a

$\alpha . \beta$

$\sf {x}^{2} - ( \alpha + \beta ) + \alpha . \beta \\ \\ \sf \: = {x}^{2} - \frac{1}{4} + ( -1) \\ \\ \sf \: multiply \: \: \: {eq}^{n} \: \: \: by \: \: \: 4 \\ \\ \boxed{ \green{{ = \sf \: 4 {x}^{2} - 1 - 4}}}$