Question

Find a quadratic polynomial ,the sum and product of whose zeroes are root 2 and -3÷2. Also find its zeros

Answer 1

Answer:

$\alpha + \beta = \sqrt{2} \: \: and \: \: \alpha \times \beta = - 3 \div 2 \\ polynomial = k( {x}^{2} - ( \alpha + \beta )x + \alpha \times \beta ) \\ = k( {x}^{2} - \sqrt{2} x - 3 \div 2) \\ = k(2 {x}^{2} - 2 \sqrt{2} x - 3) \: (where \: k \: is \: not \: equal \: to \: zero)$