Question

Find a quadratic polynomial the sum andproduct of whose zeros are 0 and minus 3 upon 5 respectively hence find the zeros

Answer 1

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.

Answer 2

HEY THERE!!

$\huge{\bold{SOLUTION:-}}$

Method of Solution:-

Given:

➡ Sum of Zeroes = 0

➡ Product of Zeroes = -3/5

Note ↔ General Formula of ax²-(a+b)x + ab

➡ Substitute the Given value in In Equation

→ ax²-(a+b)x + ab

→ x²-(0)x +(-3/5)

→ x²-3/5

Here, Quardratic Equation → x²-3/5

Solving by using Algebraic identity→

➡ (a+b)(a-b)

➡ x²-3/5

→ x²-(√3/√5)²

→ (x+√3/√5)(x-√3/√5)

f(x) → 0

Now, (x+√3/√5)= 0

•°• x = -√3/√5

Now, (x-√3/√5) = 0

•°• → x = √3/√5

Hence, Required Zeroes are ± √3/√5.