Question

(-2,-3) are zeros of the polynomial of the form ax²+bx+c, find the factor of it.​

Answer 1

Step-by-step explanation:

$given \: zeroes \: are \: - 2 \: and \: - 3 \\ \: let \: they \: be \: \alpha = - 2 \: and \: \beta = - 3 \\ \: we \: know \: that \: \\ \: if \: \alpha \: and \: \beta \: are \: the \: zeroes \: then \: the \: polynomial \: is \: \\ \: k( {x}^{2} - ( \alpha + \beta )x + \alpha \beta ) \: \\ = > k( {x}^{2} - ( - 2+ ( - 3))x + ( - 2)( - 3)) \\ \: = > k( {x}^{2} - ( - 5)x + (6)) \\ \: = > k( {x}^{2} + 5x + 6) \\ \: if \: k = 1 \: then \: the \: required \: polynomial \: is \\ \: {x}^{2} + 5x + 6. \\ \: the \: factoisation \: is \: (x + 2)(x + 3)$