Question

find quadratic polynomial whose zeroes are 2 and -1
uit​

Answer 1

Step-by-step explanation:

$Let, \: \alpha \: and \: \beta \: be \: the \: zeroes \:of \: the \: quadratic \: polynomial$

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

$\textit {Sum \: of \: zeroes = } \alpha + \beta = 2 - 1 = 1$

$\textit{Product \: of \: its \: zeroes} = \alpha \times \beta = 2 \times ( - 1) = - 2$

We know that,

${x}^{2} - ( \alpha + \beta )x + ( \alpha \times \beta )$

${x}^{2} - x - 2 = 0$

Hence this is required quadratic equation.

VERIFICATION

${x}^{2} - x - 2 = 0$

${x}^{2} - 2x + x - 2 = 0$

$x(x - 2) + 1(x - 2) = 0$

$(x + 1)(x - 2) = 0$

$x = - 1 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: \: x = 2$

Hence verified