Question

find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
x^2-2

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Answer 1

Solution :

First of all, factorise : x² - 2

• 2 can be written as (√2 )²  

Now,

→ x² - (√2 )²  

∵ a² - b² =  ( a + b ) ( a - b )

= ( x + √2 ) ( x - 2 )

TO FIND THE ZEROES :

• x + √2 ,, x = - √2
• x - √2 ,, x = √2

VERIFICATION :

a = 1 ; b = 0 ; c = - 2

Now,

sum of zeroes = - b/a

⇒ √2 + ( - √2 ) = 0/1

⇒ 0 = 0

∴ L.H.S = R.H.S

Also,

Product of zeroes = c/a

⇒ √2 × ( - √2 ) = -2/1

⇒ - 2 = - 2

∴ L.H.S = R.H.S

Hence proved!

$\rule{200}2$