Question

if alpha and beta are zeroes of the polynomial (t)square-t-4. from a quadratic polynomial whose zero are 1/alpha and 1/beta.

Answer 1

FINAL ANSWER:
$4 {t}^{2} + t - 1 = 0$
Understanding :
1) Quadratic Equations

Steps:
1) Replace t with 1/t to get the polynomial having zeroes as 1/α and 1/β .

2)
Given equation:
${t}^{2} - t - 4 = 0$
Replace t with 1/t.
Then, we get
${ (\frac{1}{t} )}^{2} - \frac{1}{t} - 4 = 0 \\ = > 1 - t - 4 {t}^{2} = 0 \\ = > 4 {t}^{2} + t - 1 = 0$