Question

The quadratic polynomial the sum and product of whose zeroes are 0 and √5 respectively is (a)x²-√5 (b)x²+√5 (c)x²-5 (d)x²+5

Answer 1

Step-by-step explanation:

Hey !!

Sum of zeroes = 0

And,

Product of zeroes = -3/5.

Therefore,

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

X² - ( 0 ) X + (-3/5 )

X² - 3/5.

Hence,

Required quadratic polynomial = X² - 3/5.

=> X² - 3/5 = 0

=> 5X² - 3 = 0

=> (√5 X )² - (√3 )² = 0

=> ( √5X + √3 ) ( √5 X - √3 ) = 0

=> ( √5 X + √3 ) = 0 or ( √5X - √3 ) = 0

=> X = -√3/√5 or X = √3/√5.

Hence,

-√3/√5 and √3 / √5 are the two zeroes of the quadratic polynomial X² - 3/5.