Question

Find the quadratic polynomial if the sum and product of its zeroes are 1⁄4 and -1?

Answer 1

Step-by-step explanation:

$sum\: of \:zeros\:= \frac{ - b}{a} = \frac{1}{4} \\ product \: of \: zeros = \frac{c}{a} = \frac{ - 1}{1} = \frac{ - 1 \times 4}{1 \times 4} = \frac{ - 4}{4} \\ we \: have \: to \: equal \: the \: value \: of \: a \: in \: both \: conditions \\ so \: \: we \: get \: \\ a = 4 \: \: \: b = - 1 \: \: \: c = - 4 \\ quadratic \: equation = a {x}^{2} + bx + c \\ = 4 {x}^{2} - x - 4$

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