Question

if alpha and beta are the zeros of x^2-3x+7 find a polynomial whose zeros are 1/alpha and 1/beta​

Answer 1

Answer:

X² - 3X + 7

Here,

A = 1 , B = -3 and C= 7

Sum of zeroes = -B/A

Alpha + Beta = -(-3)

Alpha + Beta = 3 --------(1)

And,

Product of zeroes = C/A

Alpha × Beta = 7 -------(2)

Zeroes of the other quadratic polynomial are 1/Alpha and 1/Beta.

Sum of zeroes of the other quadratic polynomial = 1/Alpha + 1/Beta = Beta + Alpha / Alpha × Beta

=> 3/7

And,

Product of zeroes = 1/Alpha × 1/Beta = 1/Alpha × Beta = 1/7

Therefore,

Required quadratic polynomial = X²-(Sum of zeroes)X + Product of zeroes

=> X² - (3/7)X + 1/7

=> X² - 3X/7 + 1/7

=> 7X² - 3X + 1.

HOPE IT WILL HELP U