Question

find the quadratic polynomial whose alpha beta are root 5 and minus root 5​

Answer 1

Step-by-step explanation:

Let $\alpha$ and $\beta$ are the roots of the equation

$\alpha = \sqrt{5}$

$\beta = - \sqrt{5}$

Sum of the roots,

$\alpha + \beta = \sqrt{5} - \sqrt{5} = 0$

Product of the roots,

$\alpha \beta = \sqrt{5} \times - \sqrt{5} = - 5$

The quadratic polynomial is in the form of,

${x}^{2} + ( \alpha + \beta )x + \alpha \beta$

${x}^{2} - 0x - 5$

${x}^{2} - 5$