Question

If alpha and beta are zeroes of 4x2 - x - 4, find
quadratic polynomial whose zeroes are
1/2alpha and 1/2beta


plzzz jaldi kar do​

Answer 1

Answer:

$({ \frac{1}{x} })^{2} - \frac{1}{2x } - 4$

Step-by-step explanation:

The roots are symmetric.

So,

$f(x) = {4x}^{2} - x - 4$

$f( \alpha ) = 0 \: and \: f( \beta ) = 0$

$x = \frac{1}{2 \alpha }$

$\alpha = \frac{1}{2x}$

Now, also

$f( \alpha ) = 0 \: and \: f( \beta ) = 0$

$f( \alpha ) = 4( { \frac{1}{2x} })^{2} - \frac{1}{2x} - 4$

$f( \alpha ) = ({ \frac{1}{x} })^{2} - \frac{1}{2x} - 4$