Question

Fine equality equality polynomial the sum and product of whose zeros are - 3 and 2 respectively

Answer 1

AnsWer

$\tt{ k( {x}^{2} + 3x + 2.)}$

Explanation

$\: \: \tt{ Sum \: of \: zeros \: -3.}$

$\: \: \tt{Product \: of \: zeros \: 2.}$

It's means,

$\\ \: \: \: \alpha + \beta = - 3. \\ \: \: \: \alpha \times \beta = 2.$

$\: \: \: \tt{Let's \: Sum \: of \: zeros \: be \: S \: and } \\ \: \: \: \tt{product \: of \: zeros \: be \: P.}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{K( {x}^{2} - sx + p )}$

Here, k is constant term.

$\leadsto \tt{K( {x}^{2} - ( - 3)x +( 2) )}$

$\leadsto \tt{K( {x}^{2} + 3x + 2. )}$

Some information

$\tt{Sum \: of \: zeros = \alpha + \beta = \frac{ - b}{a} }$

$\\ \tt{Produc t \: of \: zeros = \alpha \times \beta = \frac{c}{a} }$