Question

Write the quadratic polynomial whose zeros are negative four by 5 and 1 by 3

Answer 1

Let α and β are the zeroes of the quadratic polynomial

Given :-

$\alpha =\frac{-4}{5}\\\\\beta=\frac{1}{3}$

if, α and β are the roots or zeroes of quadratic equation, then the equation is in the form of

$x^{2} -(\alpha +\beta)x+\alpha \beta=0$

sum of zeroes or roots = α +β

product of zeroes or roots = αβ

$x^{2}-(\frac{-4}{5}+\frac{1}{3})x+(\frac{-4}{5}) (\frac{1}{3} )=0 \\\\x^{2}-(\frac{-7}{15})-\frac{4}{15}=0 \\\\x^{2} +\frac{7}{15}-\frac{4}{15}=0\\\\15x^{2} +7-4=0$