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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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!
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