Question

Form a quadratic polynomial if :-
sum of zero = -1/2
product of zero = 1/3.​

Answer 1

Step-by-step explanation:

$given \: that \\ \: the \: sum \: of \: zeroes = \frac{ - 1}{2} \\ \: product \: of \: zeroes = \frac{1}{3} \\ \: we \: know \: that \: \\ \: if \: \alpha \: and \: \beta \: are \: the \: zeroes \: then \: the \: quadratic \: polynomial \: is \: \\ \: k ({x}^{2} - ( \alpha + \beta )x + \alpha \beta ) \\ \: = > k( {x}^{2} - ( \frac{ - 1}{2} )x + \frac{1}{3} ) \\ \: = > k( {x}^{2} + \frac{1}{2} x + \frac{1}{3} ) \\ \: = > \frac{k(6 {x}^{2} + 3x + 2) } {6} \\ \: if \: k = 6 \: then \: the \: required \: polynomial \: is \\ \: 6 {x}^{2} + 3x + 2$