Question

FIND THE ZEROES OF THE QUADRATIC POLYNOMIAL x2 - (root3 +1) x+root3 and verify the relations between the zeroes and its co efficients...


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Answer 1

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Answer 2

Answer :

The equation is given to be : p(x) = x² - (√3 + 1)x + √3

To find the zeros of the given equation, Equate the given p(x) = 0

⇒ x² - (√3 + 1)x + √3 = 0

⇒ x² - √3x - x + √3 = 0

⇒ x(x - √3) - 1(x - √3) = 0

⇒ (x - √3)(x - 1) = 0

⇒ x = 1 and x = √3

⇒ α = 1 and β = √3

Now, α + β = 1 + √3

-b/a = 1 + √3

⇒ α + β = -b/a

And, β = √3

So, β = c/a