Question

find a quadratic polynomial each with the given numbers as a sum and product of its zeros respectively [¡] 1 /4 ,-1​

Answer 1

Showing results for find a quadratic polynomial each with the given numbers as a sum and product of its zeroes respectively [¡] 1 /4 ,-1

Search instead for find a quadratic polynomial each with the given numbers as a sum and product of its zeros respectively [¡] 1 /4 ,-1

Answer 2

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

Let the polynomial be

$ax²+bx+c$ , and it's zeroes be

$\alpha$ and $\beta$ .

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

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

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

$\therefore ~ Quadratic ~ polynomial ~ is ~ 4x²-x-4$