Question

The sum and product of the zeros of a quadratic polynomial are -1/2 and -3 respectively. What is the quadratic polynomial. *



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Answer 1

Solution :-

$let \: the \: zeros \: of \: quadrztic \: polynomial \: be \\ \alpha , \: \: \beta \\ \alpha + \beta = \frac{ - 1}{2} \\ \alpha \beta = - 3 \\ the \: required \: quadratic \: polynmial \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ {x }^{2} - ( \frac{ - 1}{2} ) x+ ( - 3) = 0 \\ {x}^{2} + \frac{1}{2} x - 3 = 0 \\ multiplying \: by \: 2 \\ 2 {x}^{2} + x - 6 = 0$

Thanks for the question bro ❤️❣️✌️✍️

Answer 2

Step-by-step explanation:

Let a+b=-1/2 ab=-3

Quadratic polynomial =x2-(a+b)x+ab

=x2-(-1/2)x+(-3)

=x2+1/2x-3

=2x2+1x-6

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2

=1/2 (2x2+x-6)