Question

Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2
respectively. Also, find its zeroes.

Answer 1

Step-by-step explanation:

$\alpha + \beta = \sqrt{2} \\ \alpha \beta = \frac{ - 3}{ 2} \\ \\ {x}^{2} - ( \alpha + \beta ) {x} + \alpha \beta = 0 \\ \\ = > {x}^{2} - \sqrt{2} x - \frac{3}{2} = 0 \\ = > 2 {x}^{2} - 2 \sqrt{2} x - 3 = 0 \\ = > 2 {x}^{2} - 3 \sqrt{2}x + \sqrt{2} x - 3 = 0 \\ = > \sqrt{2} \: \sqrt{2} x( \sqrt{2} x - 3) + 1( \sqrt{2} x - 3) = 0 \\ = ( \sqrt{2} x + 1)( \sqrt{2x} - 3) = 0 \\ = > \sqrt{2} x + 1 = 0 \: \: or \: \sqrt{2} x - 3 = 0 \\ = > \sqrt{2} x = - 1 \: \: \: or \: \sqrt{2} x = 3 \\ = > x = \frac{ - 1}{ \sqrt{2} } \: \: or \: \: x = \frac{3}{ \sqrt{2} }$