Question

find the quadratic polynomial for the zeroes alpha and bheta for given case 2,-1
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Answer 1

$\alpha = 2 \ \: \beta = - 1$

$sum \: of \: zeroes \: = \alpha + \beta \\ = 2 - 1 \\ = 1 \\ = \frac{ - b}{a} \\ = \frac{1}{1}$

$product \: of \: zeroes = \alpha \beta \\ = 2 \times - 1 \\ = - 2 \\ = \frac{c}{a} \\ = \frac{ - 2}{1}$

Therefore , a=1 ,b=1 ,c=(-2)

the required quadratic equation is,

=ax^2+bx+c

=(1)x^2+(1)x+(-2)

=x^2 +x-2