Question

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

$\frac{1}{4},-1$

Answer 1

$\frac{1}{4},-1$

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

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

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

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

$\therefore$ Quadratic polynomial is $4x^2-x-4$.