Question

if Alpha be the number of person who take junk food beta be the person who take food at home and alpha and beta are the zeros of quadratic polynomial f x is equal to x square - 3 x + 2 then find a quadratic polynomial whose zeros are 1 by 2 alpha + beta and 1 by 2 Beta + Alpha which way of taking food you prefer and why​

Answer 1

${x}^{2} - 3x + 2 = 0 \\ {x}^{2} -2x - x + 2 = 0 \\ x(x - 2) - 1(x - 2) = 0 \\ (x - 1)(x - 2) = 0 \\ x = 1 \: \: x = 2 \\ let \: \: \alpha = 1 \: \: \beta = 2 \\ \\ \frac{1}{2 \alpha } + \beta = \frac{1}{2} + 2 = \frac{5}{2} \\ \frac{1}{2 \beta } + \alpha = \frac{1}{4} + 1 = \frac{5}{2} \\ \\ {x}^2 -5x + \frac{25}{4} = 0 \\ 4 {x}^{2} - 20x + 25 = 0...... \: this \: is \: the \: required \: equation$

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