Question

Find the quadratic equation whose roots are reciprocals of the roots of the equation 7x^2-2x+9=0

Answer 1

Heya !!!

Let Alpha and Beta are the roots of the quadratic equation 7X² -2X + 9

P(X) = 7X² -2X + 9

Here,

A = 7 , B = -2 and C = 9

Sum of zeroes = -B/A

Alpha + Beta = - (-2)/7

Alpha + Beta = 2/7 --------(1)

And,

Product of zeroes = C/A

Alpha × Beta = 9/7 --------(2)

According to question,

Roots of the other quadratic which is reciprocal to alpha and Beta is 1/Alpha and 1/Beta

Sum of zeroes = 1/Alpha + 1/Beta

=> Beta + Alpha / Alpha × Beta

=> 2/7/9/7

=> 2/9

And,

Product of zeroes = 1/Alpha × 1/Beta

=> ( 1)/ Alpha × Beta

=> 1/9/7

=> 1/9 × 1/7

=> 1/63

Therefore,

Required quadratic polynomial =

=> X²-(Sum of zeroes )X + Product of zeroes

=> X²-(2/9)X + 1/63

=> X² - 2X/9 + 1/63

=> 63X² - 14X + 1 = 0

★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★

Answer 2

Hi,

Please see the attached file!


Thanks