Question

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

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

Answer 1

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

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

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

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

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

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