Question

$\alpha \: and \: \beta$are the zeros of a quadratic polynomial f(t) =t^2- 4 t + 3 find the polynomial whose zeros are double of zeros of f(t)​

Answer 1

Step-by-step explanation:

zeros of f(t) are t² - 3t - t + 3

=> t (t - 3) - 1 ( t - 3)

=> (t - 3)(t - 1) = 0

t = 3 and t = 1 are the zeros of the given polynomial f(t)

now let p(x) be tne polynomial whose zeros are double of that of f(t)

therefore zeros of p(t) = 6 and 2

hence p(t) = t² - t ( sum of zeros ) + product of zeros

p(t) = t² - t (6+1) + 6*1

p(t) = t² - 7t + 6