Question

If αand β are the two zeros of the polynomial 6 y 2 -7Y + 2 , find the quardtraic polynomial whose zeroes are 1/α and 1/β

Answer 1

Heya !!!

P(X) = 6Y² -7Y + 2

Here,

A = 6 , B = -7 and C = 2

Sum of zeroes = -B/A

Alpha + ß = 7 /6

And,

Alpha × ß = C/A

Alpha × ß = 2 /6 = 1/3

Sum of zeroes of quadratic polynomial whose zeroes are 1/Alpha and 1/ß

Sum of zeroes = 1/Alpha + 1/ß = ß + Alpha/Alpha × ß =

=> 7/6 / 1/3



=> 7/6 × 3/1

=> 7/2

And,

Product of zeroes = 1/Alpha × 1/ß = 1/Alphaß = 1/1/3


=> 1/1 × 1/3

=> 1/3

Therefore,

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

=> X² - (7/2) X + 1/2

=> X²-7X/2 + 1/3

=> 6X²-21X + 6

★ HOPE IT WILL HELP YOU ★