Question

Question 2 (iii)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

$0,\sqrt{5}$

Answer 1

$0,\sqrt{5}$

Let the polynomial be $a{x}^2+bx+c$, and its zeroes be $\alpha$ and $\beta$.

$\alpha +\beta =0=\frac{0}{1}=\frac{-b}{a}$

$\alpha \beta =\sqrt{5}=\frac{\sqrt{5}}{1}=\frac{c}{a}$

$\therefore$ a = 1, b = 0, c = $\sqrt{5}$

$\therefore$ Quadratic polynomial is $x^2+\sqrt{5}$.