Question

2) Find a quadratic polynomial the sum and product of whole zero's are -1/4 and 1/4​

Answer 1

$Let \: \alpha \: and \: \beta \: are \: two \\zeroes \: of \: a \: Quadratic \: polynomial$

$i) Sum \: of \: the \: zeroes =\frac{-1}{4}$

$\implies \alpha + \beta = \frac{-1}{4}\: --(1)$

$ii) Product\: of \: the \: zeroes =\frac{1}{4}$

$\implies \alpha \beta = \frac{1}{4}\: --(2)$

$\red{ Form \:of \: a \: Quadratic \: polynomial }$

$k[ x^{2} - (\alpha + \beta )x + \alpha \beta ]$

$= k [ x^{2} - \Big(\frac{-1}{4}\Big) x + \Big( \frac{1}{4}\Big) ]$

$For \: all \: real \: values \:'k' \: it \: is \: true.$

$If \: k = 4 \: then \: the \: polynomial \: is \\4x^{2} + x + 1$

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