Question

Find the quadric polynomial with the given no. As the sum and product of zeroes are 1/4, -1

Answer 1

Answer:

$sum \: of \: zeroes \:( \alpha + \beta ) = \ \binom{1} {4} \\ \\ product \: of \: zeroes \: ( \alpha \beta ) = - 1 \\ \\ quadratic \: polynomial = k(x2 - ( \alpha + \beta )x + \alpha \beta \\ \\ k(x2 - \binom{1}{4} x - 1) \\ \\ lcm = 4 \\ \\ we \: get \: 4x2 - x - 4 \\ \\ p(x) = 4x2 - x - 4$

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