Question

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

4, 1

Answer 1

4, 1

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

$\alpha +\beta =4=\frac{4}{1}=\frac{-b}{a}$
$\alpha \beta =1=\frac{1}{1}=\frac{c}{a}$

$\therefore$ a = 1, b = -4, c = 1

Therefore, the quadratic polynomial is $x^2-4x+1$.