Question

Find the quadratic polynomial if its zeroes are 0, √5.​

Answer 1

A quadratic polynomial can be written using the sum and product of its zeroes as: x² + (α+β) + αβ = 0

Where α and β are the roots of the equation.

$\begin{gathered}\sf \: \: \: \: \: \bullet \alpha = 0 \\ \: \: \:\: \: \sf \bullet \beta = root 5\end{gathered}$

$\bf \underline{Equation}$

$\boxed{x {}^{2} + \sqrt{5}x = 0}$

$\begin{gathered}\\ \bf \therefore {\underline{quadratic \: polinomial \: is \: {x}^{2} + \sqrt{5} x }}\end{gathered}$

Answer 2

Answer:

A quadratic polynomial can be written using the sum and product of its zeroes as: x² + (α+β) + αβ = 0

Where α and β are the roots of the equation.

$\begin{gathered}\begin{gathered}\sf \: \: \: \: \: \bullet \alpha = 0 \\ \: \: \:\: \: \sf \bullet \beta = root 5\end{gathered}\end{gathered}$

∙α=0

∙β=root5