Question

Write the polynomial whose zeroes are -5 and 4 *

Answer 1

$Let \: \alpha \:and \:\beta \: are \: two \: zeroes$

$of \: a \: polynomial$

$Given \: \alpha = -5 \:and \:\beta = 4$

$i) \alpha + \beta$

$= -5 + 4$

$= -1$

$ii) \alpha \beta$

$= (-5 ) \times 4$

$= -20$

$\blue { The \: form \:of \: Quadratic \: polynomial }$

$\blue{whose \: zeroes \: are \:\alpha \:and \:beta\:is}$

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

$= k[ x^{2} - (-1)x + (-20)]$

$= k(x^{2} +x - 20 )$

We can put different values of k .

When k = 1 ,

The Quadratic polynomial will be x²+x-20.

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