Question

find the quadratic polynomial whose sum and product of zeros are 1 by 4 and minus 1 respectively

Answer 1

Answer:

The required quadratic polynomial is $\frac{1}{4}[x^2+3x-1]$

Step-by-step explanation:

Formula used:

The quadratic polynomial having zeros

$\alpha\: and \:\beta$ is

$x^2-(\alpha+\beta)x+\alpha\beta$

Given zeros are 1/4 and -1

sum of the zeros

$= \frac{1}{4}+(-1)\\\\=\frac{1-4}{4}\\\\=\frac{-3}{4}$

product of the zeros

$=\frac{1}{4}*(-1)\\\\= \frac{-1}{4}$

The required quadratic polynomial is

x² -(sum of the zeros)x+(product of the zeros)

$=x^2-(\frac{-3}{4})x+(\frac{-1}{4})\\\\=x^2+\frac{3}{4}x-\frac{1}{4}\\\\=\frac{1}{4}[x^2+3x-1]$